gs13 abstracts - siam.org · 70 gs13 abstracts cal/ﬂuidﬂowprobleminporousmediaissolvedinasingle...

68 GS13 Abstracts

Approximation of Transport Processes UsingEulerian-Lagrangian Techniques

Transport processes are common in geoscience applica-tions, and find their way into models of, e.g., the atmo-sphere, oceans, shallow water, subsurface, seismic inver-sion, and deep earth. Our objective is to simulate transportprocesses over very long time periods, as needed in, e.g.,the simulation of geologic carbon sequestration. A goodnumerical method would be locally mass conservative, pro-duce no or minimal over/under-shoots, produce minimalnumerical diffusion, and require no CFL time-step limit forstability. The latter would allow better use of parallel com-puters, since time-stepping is essentially a serial process.Moreover, it would be good for the methods to be of highorder accuracy. Our approach is to develop locally conser-vative Eulerian-Lagrangian (or semi-Lagrangian) methodscombined with ideas from Eulerian WENO schemes, sincethey have the potential to attain the desired properties.

Todd ArbogastDept of Math; C1200University of Texas, Austinarbogast@ices.utexas.edu

The Spatiotemporal Dynamics of Waterborne Dis-eases

Dynamics of waterborne diseases in space and time is stud-ied via multi-layer network models, consisting of coupledODEs. They account for the interplay between epidemio-logical dynamics, hydrological transport and long-distancedissemination of pathogens due to human mobility, de-scribed by gravity models. Conditions for the outbreakof an epidemic are given in terms of the dominant eigen-value of an appropriate reproduction matrix, while the ini-tial disease distribution is linked to the dominant eigen-vector. The theory is tested against epidemiological dataof the extensive cholera outbreaks occurred in KwaZulu-Natal (South Africa) during 2000-2001 and in Haiti during2010-2012.

Marino GattoPolitecnico di Milanogatto@elet.polimi.it

Career Award Lecture: Some Successes and Chal-lenges in Coastal Ocean Modeling

The coastal ocean is rich with physical and biological pro-cesses, often occurring at vastly different scales. In thistalk, we will outline some of these processes and their math-ematical description. We will then discuss the current stateof numerical methods for coastal ocean modeling and re-cent research into improvements to these models, focusingon accuracy and efficiency for high performance comput-ing. We will also highlight some of the successes of thesemodels in simulating complex events, such as hurricanestorm surges. Finally, we will outline several interestingchallenges which are ripe for future research.

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

Junior Scientist Award Lecture: Interpreting Geo-logical Observations Through the Analysis of Non-linear Waves

Geological and environmental systems are rich in examplesof self-organization and pattern formation. These patternscontain information about processes as diverse as seawa-ter intrusion into coastal aquifers, the long-term safety ofgeological CO2 storage, and the formation of the oceaniccrust. I will discuss how important observations in thesethree areas can be explained by non-linear waves. Thisillustrates the potential of the mathematical analysis ofnon-linear waves to contribute to our understanding of fun-damental geological phenomena and applied environmentalproblems.

Marc A. HesseUniversity of TexasDepartment of Geological Sciencesmhesse@jsg.utexas.edu

An Unstructured Grid Model Suitable for FloodingStudies with Applications to Mega-tsunamis

Mega-thrust earthquakes and tsunamis cause untold de-struction. In this talk a new finite volume unstructuredgrid tsunami model is presented. The model is a finitevolume analogue of the P1nc-P1 finite element, in whichmass conservation is guaranteed not only in a global sense,but within each cell. The model conserves momentum, andaccurately handles flooding and drying problems. Resultsfrom the Indian Ocean and Japanese Tsunami comparewell with flooding and run-up data.

Julie PietrzakFaculty of Civil Engineering and GeosciencesDelft University of Technologyj.d.pietrzak@tudelft.nl

Haiyang Cui, Guus StellingDelft University of Technologyh.cui@tudelft.nl, g.stelling@ct.tudelft.nl

Data Assimilation in Global Mantle Flow Mod-els:Theory, Modelling and Uncertainties to Recon-struct Earth Structure Back in Time

The ability to extract the history of motion associated withlarge-scale geologic structures that are now imaged seismi-cally in the Earth’s interior, such as plumes and subductingslabs, is crucial to constrain the fundamental deformationprocesses of mantle convection. Here we show how fluiddynamic inverse theory, based on a variational approach,can be applied in a global circulation model of the mantleto project Earth structure back in time. We present thebasic theory of the forward and inverse problem, reviewgeologic constraints, provide computational considerationsrelevant to the global flow problem with about 1 billionfinite elements, and discuss uncertainties. The latter re-strict the problem in practice, as our knowledge of deepEarth structure and its interpretation in terms of dynam-ically relevant buoyancy anomalies is necessarily limited.

Hans-Peter BungeDepartment of Earth and Environmental Sciences, LMU

GS13 Abstracts 69

Munichbunge@geophysik.uni-muenchen.de

Data Assimilation and Inverse Modeling in EarthSystem Sciences

Physical theories in the Earth System sciences are designedto explain and possibly predict natural phenomena. Both,the explanation and prediction necessarily include a quan-titative representation of the natural system state. Quan-titative assessment of the actual, true, state is fundamen-tally achievable only by measurements. The theories andmodels based on them are consequently designed to ex-plain and predict the measurements. A synergy of themodels and measurements is necessary for achieving suchgoal. Methodology of data assimilation and inverse model-ing provides objective means for that purpose. An overviewof the currently used methodology will be presented, in-cluding examples of application in atmospheric sciences indomain of cloud analysis and modeling and tropical cyclonemodeling and prediction.

Tomislava VukicevicNOAAAOML Hurricane Research Division, MiamiTomislava.Vukicevic@noaa.gov

Efficient Numerical Numerical Computation ofMulti-Phase Flow in Porous Media

Appropriate models, accurate discretization schemes andefficient solvers for the arising linear systems are the ba-sis for any numerical simulation. In this talk I will addressthese aspects by first considering a model for compositionaltwo-phase flow with equilibrium phase exchange that isable to handle phase appearance/disapperance properly.Then a new fully-coupled discontinuous Galerkin schemefor two-phase flow with heterogeneous capillary pressurewill be presented. The third part of the talk is devoted tothe efficient solution of the arising linear systems by meansof algebraic multigrid methods. All numerical schemeshave been implemented in the Distributed and Unified Nu-merics Environment and have been scaled up to 300000cores. This is joint work with Olaf Ippisch and RebeccaNeumann.

Peter BastianInterdisciplinary Center for Scientific ComputingUniversity of Heidelbergpeter.bastian@iwr.uni-heidelberg.de

A Mixed and Galerkin Finite Element Formulationfor Coupled Poroelasticity

The numerical treatment of coupled poroelasticity is a de-manding task because of the instabilities affecting the porepressure solution. A combination of Mixed and GalerkinFinite Element methods is employed to obtain stable nu-merical solutions at the interface between different mate-rials. A comparison of the performance of monolithic andsequential schemes in solving the algebraic systems aris-ing from the balance equations is presented. Some resultsrelative to real field large scale simulations are finally dis-cussed.

Nicola Castelletto

DMMMSAUniversity of Padovacastel@dmsa.unipd.it

Carlo Janna, Massimiliano FerronatoDept. ICEA - University of Padovacarlo.janna@unipd.it, massimiliano.ferronato@unipd.it

Coupled Geomechanics and Flow for UnstructuredNaturally Fractured Reservoir Models

We consider unstructured reservoir models composed ofa deformable saturated matrix and a network of naturalfractures. A finite-volume method is used for the flow.Galerkin finite elements are used to discretize the poro-elasto-plasticity equations. We account for normal andshear stresses on the fracture surfaces. The correspond-ing nonlinear coupled equations are solved using eitherthe sequential-implicit fixed-stress approach, or the fully-implicit method. The framework is demonstrated usingseveral test cases with discrete fracture models.

Timur T. GaripovDepartment of Energy Resources Engineering,Stanford Universitytgaripov@stanford.edu

Hamdi TchelepiStanford UniversityEnergy Resources Engineering Departmenttchelepi@stanford.edu

Mechanics of Fluid Injection into DeformablePorous Materials

Poroelasticity, where the mechanical deformation of aporous solid is coupled to internal fluid flow, has beenstudied intensely in geophysics in the context of pressurebuildup during fluid injection, such as in carbon seques-tration or enhanced oil recovery. Here, we develop a novelexperimental system that allows us to visualize and quan-tify the dynamic, flow-driven deformation of a quasi-two-dimensional poroelastic material. We use it to study thecoupling between fluid injection and mechanical deforma-tion patterns.

Christopher W. MacMinnMITMechanical Engineeringchristopher.macminn@yale.edu

Eric DufresneYale UniversityNew Haven, CT, USAeric.dufresne@yale.edu

John S. WettlauferYale Universityjohn.wettlaufer@yale.edu

A Finite Volume Method for the Solution of FluidFlows Coupled with the Geomechanics of Compact-ing Porous Media

A numerical approach in which a coupled geomechani-

70 GS13 Abstracts

cal/fluid flow problem in porous media is solved in a singlegrid using a Finite Volume Method is advanced. The pos-sibility of using a unique grid and the same conservativemethod for both problems renders to the scheme robustnessand generality. Details of the coupling strategy are also ad-dressed. The novel developments offer an interesting routefor solving coupled problems in a unified approach usingfull conservative schemes.

Clovis R. MaliskaMechanical Engineering DepartmentFederql University of Santa Catarinamaliska@sinmec.,ufsc.br

Alessandro Dal PizzolFederal University of Santa CatarinaMechanical Engineering Departmentalessandro.pizzol@sinmec.ufsc.br

Solution Strategies for Coupled Geomechanical andFlow Problems Recent Experiences

Many geoscience problems involve coupled THM (thermal-hydrodynamic-mechanical) processes. The strength of cou-pling has varying degrees, ranging from problems that canbe solved sequentially to those requiring full nonlinear cou-pling. The selection of the method and the degree of cou-pling are highly problem-dependent. The best strategy forTHM processes depends critically on the physics of theproblem. We will give a survey of the methods (used incoupled reservoir geomechanics) and discuss examples ofour experience with their stability and implementation.

A . (Tony) Settari

University of Calgaryasettari@taurusrs.com

A Fully Coupled Multiphase Flow and Geomechan-ics Solver for Highly Heterogeneous Porous Media

This paper introduces a fully coupled multiphase flow andgeomechanics solver that can be applied to modeling highlyheterogeneous porous media. In this work, we developeda coupled multiphase flow and geomechanics solver thatsolves fully coupled governing equations, namely pressure,velocity, saturation, and displacement equations. Thesolver can deal with full tensor permeability and elasticmoduli for modeling a highly heterogeneous reservoir sys-tem.

Daegil YangTexas A&M Universitydaegil.yang@gmail.com

George MoridisLawrence Berkeley National Laboratorygjmoridis@lbl.gov

Thomas BlasingameTexas A&M Universityt-blasingame@tamu.edu

A Domain Decomposition-Based Parallel Software

for Data Assimilation in the Mediterranean Sea

OceanVar is a data assimilation (DA) software which isbeing used in Italy within the Mediterranean ForecastingSystem (MFS) to combine observational data (SLA, SST,Argo-floats profiles) with backgrounds produced by com-putational models of ocean currents of the MediterraneanSea (namely, the NEMO framework). OceanVAR imple-ments a three-dimensional variational scheme. We discussthe design of a fully parallel version of OceanVar, basedon domain decomposition approach, which is able to faceto the ever greater multi-level parallelism and scalabilityof the current and the next generation of leadership com-puting facility systems (multi processors, many core andGPUs), while fulfilling the specific requirements of Ocean-Var within the MFS.

Luisa D’ AmoreUniversity of Naples Federico II Naples, ITALYMathematics and Applicationsluisa.damore@unina.it

Rossella ArcucciEuro-Mediterranean Center on Climate ChangeCMCC- Lecce, Italyrossella.arcucci@cmcc.it

Luisa CarracciuoloItalian National Research Council (CNR)ITALYluisa.carracciuolo@itcp.cnr.it

Livia MarcellinoUniversity of Naples, ParthenopeITALYlivia.marcellino@uniparthenope.it

Almerico MurliEuro-Mediterranean Center on Climate ChangeITALYalmerico.murli@cmcc.it

Scalable Reservoir Simulation on Massively Paral-lel Computers

We investigate parallel performance for reservoir simula-tion on multiple massively parallel computing architec-tures. A deliberate strategy of performance-based devel-opment of the major types of computations encountered inreservoir simulation programs is employed. Even thoughmost operations are memory-bandwidth bound, it is pos-sible with careful implementation, to get excellent parallelefficiency to several 1000s of cores. We discuss numericalissues, scalability and parallel efficiency of reservoir sim-ulator on several very large and geologically challengingexamples.

Serguei Y. MaliassovExxonMobil URCserguei.maliassov@exxonmobil.com

Bret BecknerExxonMobil Upstream Research Companybret.l.beckner@exxonmobil.com

Vadim DyadechkoExxonMobil URCvadim.dyadechko@exxonmobil.com

GS13 Abstracts 71

Scalable Multi-Level Preconditioning Techniquesfor Variable Viscosity Stokes Flow Problems Aris-ing from Geodynamic Applications

Over long million year time scales, many geological pro-cesses can be described as incompressible, variable viscos-ity Stokes flow. Such descriptions of rock deformation arechallenging to handle as the viscosity structure is inher-ently heterogeneous and may possess both continuous anddiscontinuous local variations on the order of 109. Here weexplore the performance of a parallel matrix-free geomet-ric multi-grid preconditioner combined with several exoticcoarse grid solvers to study high resolution 3D geodynamicprocesses.

Dave MayETH Zurichdave.may@erdw.ethz.ch

Sam(oa)2, a Parallel Cache-Efficient Simulation En-vironment

We present an integrated approach for parallel adaptivegrid refinement and respective solution of PDEs. Usinga stack-and-stream system and an element order definedby the Sierpinski space filling-curve to store and processthe grid and simulation data, we obtain an inherentlymemory- and cache-efficient simulation algorithm. The lo-cality properties introduced by the Sierpinski curve are re-tained even throughout adaptive refinement and coarsen-ing of the grid, and are exploited for efficient parallelisa-tion and load balancing. We will focus on parallelisationand discuss a run-length encoding to deal with the dataexchange on the shared inter-process edges. These datainclude the numerical unknowns, refinement flags on theedges, and load balancing information. We present twotest case scenarios: A Discontinuous Galerkin solver forthe Shallow Water Equations and a coupled problem forporous media flow using FEM for the pressure equationand finite volumes for the advection term.

Kaveh RahnemaUniversity of StuttgartInstitute of Parallel and Distributed Systemsrahnema@in.tum.de

Oliver MeisterTechnische UniversitDepartment of Informatics, Scientific Computingmeistero@in.tum.de

Michael BaderTechnische Universitaet MuenchenDepartment of Informaticsbader@in.tum.de

A Parallel Server for Adaptive Geoinformation

In this talk we present ASAGI, a library that providesa simple and efficient interface to large input data setswith multiple resolutions in a high performance comput-ing context. The key feature of ASAGI is to decouple thedata management from the actual simulation by introduc-ing caching strategies on node level. Thus, for dynami-cally adaptive simulations with parallel partitions that maychange their spatial position and extent, ASAGI provides

the parameter information (material properties, topogra-phy or bathymetry data, etc.) required for adaptive refine-ment and coarsening.

Sebastian RettenbergerTechnische Universitaet MuenchenDepartment of Informatics, Chair of Scientific Computingrettenbs@in.tum.de

Alexander BreuerTechnische Universitat MunchenDepartment of Informatics, Scientific Computingbreuer@in.tum.de

Oliver MeisterTechnische Universitat Munchenmeistero@in.tum.de

Some Strategies of Linear and Nonlinear Precondi-tioning for Reactive Transport Model

We investigate block preconditioning for accelerating aNewton-Krylov method applied to a reactive transportmodel. Work by Kern and Taakili (2011) for a singlespecies with sorption is extended to the multi-species case,with complex chemistry. The block structure of the modelis exploited both at the nonlinear level, by eliminating oneunknown, and at the linear level by using block Gauss-Seidel preconditioning. A link is made between physicsbased preconditioning and the algebraic methods.

Laila AmirFaculty of Science and TechniquesCadi Ayyad University,lamir@fstg-marrakech.ac.ma

Michel KernINRIAmichel.kern@inria.fr

Abdelaziz taakilliFaculty of Science and Techniques,Errachidia, Moroccotaakili abdelaziz@yahoo.fr

High Performance Computing Using Local Time-Stepping Methods for Elastodynamics

The simulation of seismic wave propagation in heteroge-neous media requires local mesh refinements that preventthe use of finite difference schemes widely used in the oilindustry. In this talk, we will present a mesh refinementstrategy combining local time stepping and a discontinu-ous Galerkin discretization using quad elements enablingthe use of embedded Cartesian grids. We will also discusshow this regular structure can be exploited in a parallelimplementation to tackle large 3D examples.

Yohann DudouitHiePACS Projectjoint INRIA-CERFACS lab. on High Performance

72 GS13 Abstracts

Computingdudouit@cerfacs.fr

Jean-Luc BoelleTOTALjean-luc.boelle@total.com

Luc GiraudInria Bordeaux Sud-OuestJoint Inria-CERFACS lab on HPCluc.giraud@inria.fr

Florence MillotCERFACSmillot@cerfacs.fr

Sebastien PernetONERAsebastien.pernet@onera.fr

Geosounding Inversion with Bregman IterativeMethods

In this contribution, several novel algorithms for nonlin-ear inversion of electrical, electromagnetic and resistivitysoundings based on Bregman iterations are presented. Re-sults are reported of algorithm implementation for severalgeosounding methods applying Bregman distance to mini-mize the TV functional. Implemented algorithms consist ofa Taylor linearization for the forward functional, Bregmandistance applied to the regularization functional and stopcriteria. The resulting algorithms are easy to implementand do not require any optimization package. Positivityconstrained version of the algorithms are also presentedby applying projected Barzilai-Borwein method with box-constrains. A comparison of developed models for Breg-man based algorithms with those obtained with a linearprogramming package is also presented for synthetic andfield data.

Hugo HidalgoCICESE-Ciencias de la Computacionhugo@cicese.mx

Enrique Gomez-TrevinoCICESEGeofisica Aplicadaegomez@cicese.mx

Algebraic Multigrid Preconditioner for Numeri-cal Finite-Element Solutions of Electromagnetic In-duction Problems

We present a parallel nodal finite-element solver for thethree-dimensional electromagnetic modelling in anisotropicmedia. The method can be used for modelling differentcontrolled-source and magnetotelluric problems. To im-prove efficiency of the method, we have developed an alge-braic multigrid preconditioner for Krylov subspace solvers.Tests for various problems show that, compared to otherpreconditioners, our preconditioner improves the conver-gence of different solvers and reduces the execution timeby up to an order of magnitude.

Jelena Koldan, Vladimir Puzyrev, Jose Maria CelaBarcelona Supercomputing Center

jelena.koldan@bsc.es, vladimir.puzyrev@bsc.es,josem.cela@bsc.es

Unconditionally Stable Transport Solvers for TwoPhases Flow with Polymer.

We present a nonlinear Gauss-Seidel algorithm for solvingimplicitly discretized saturation equations. NGS relies onthe well-posedness of single-cell problems (residual equa-tion for one cell with all other saturations known). Uncon-ditional stability of the single-cell problem guarantees thata global solution exists for any time step. We give nec-essary and sufficient conditions on discretized flux for un-conditional stability of the single-cell problem and presentsuch flux discretizations for two-phase flow with polymerand gravitation splitting.

Xavier RaynaudSintefxavier.raynaud@sintef.no

Knut-Andreas LieSINTEF ICT, Dept. Applied MathematicsKnut-Andreas.Lie@sintef.no

Halvor Nilsen, Atgeirr RasmussenSINTEF ICThalvormoll.nilsen@sintef.no, atgeirr.rasmussen@sintef.no

Precisely, How Fast Is Your Fully Implicit Newton-Like Solver?

This work characterizes the convergence rate of Newton-like methods that are applied to solve nonlinear residualsystems arising in implicit numerical simulations. Theanalysis exploits the Asymptotic Mesh Independence Prin-ciple relating the convergence rate of discrete Newtonmethods to their infinite-dimensional counterparts. Bycharacterizing the precise evolution of the nonzero spa-tiotemporal support of the infinite-dimensional iterations,the analysis reveals the asymptotic scaling relations be-tween nonlinear convergence rate and time-step and meshsizes.

Rami M. YounisPostdoctoral Research FellowStanford Universityryounis@utulsa.edu

A Computational Method for Simulating Immis-cible Incompressible Three Phase Flow Model inHeterogeneous Porous Media

We describe a computational method for simulating three-phase immiscible incompressible flow problem in inhomo-geneous media taking the form of a nonlinear transport sys-tem with spatially varying flux functions under combinedconvective, capillary and gravity effects. Our new methodis an operator splitting procedure for decoupling the non-linear three-phase flow system with mixed and conserva-tive discretization methods leading to purely hyperbolic,parabolic and elliptic subproblems. Preliminary numericalexperiments will be also presented and discussed.

Eduardo Abreu

GS13 Abstracts 73

Instituto Nacional de Matematica Pura e Aplicada -IMPAeabreu@ime.unicamp.br

Co2 Storage Simulations Using Low ComplexModel Geometries

Complex 3D models are a potential way to precisely de-scribe the heteroeneous flow paths in a reservoir, but theuncertainties of material parameters are quite large. Dueto long simulation times, 3D approaches only allow a smallnumber of realizations. Thus, we perform Monte-Carlosimulations using simplified model grids of lower complex-ity to describe the fate of CO2 at the Ketzin test site lo-cated in Germany.

Norbert BottcherTU Dresdennorbert.boettcher@ufz.de

Wenqing WangDepartment of Environmental InformaticsHelmholtz Centre for Environmental Researchwenqing.wang@ufz.de

Bjorn Zehner, Uwe-Jens GorkeHelmholtz-Centre for Environmental Research - UFZbjoern.zehner@ufz.de, uwe-jens.goerke@ufz.de

Olaf KolditzHelmholtz Centre for Environmental Researcholaf.kolditz@ufz.de

A Conservative Numerical Methodology for Multi-phase Flow in Heterogenous Porous Media Allow-ing Changes in Porosity

In this work we present a conservative numerical methodol-ogy for simulating multiphase-flow in highly heterogenousporous media, which allows changes of the porosity fieldin time and space. This methodology combines stabilizedmixed-hybrid finite elements for the flow subsystem (ve-locity and pressure) with a semi-discrete central schemefor the transport problem, based on a generalization of theKurganov and Tadmor (KT) scheme. This methodologyis proposed to be used as a block for coupling multiphaseflows with geomechanics.

Maicon R. CorreaNational Laboratory of Scientific ComputingLNCC, Brazilmaicon@ime.unicamp.br

Marcio BorgesNational Laboratory of Scientific ComputationLNCC/MCTPetropolismrborges@lncc.br

Jesus ObregonNational Laboratory of Scientific ComputingLNCC/MCTalexei@lncc.br

Using Coupled Implicit and P-Adaptive Discontin-uous Galerkin Method to Model Miscible Displace-ment with Adverse Mobility Ratio

Many EOR or stimulation processes require an accurateestimation of the distribution of the injected fluid. Tra-ditional reservoir simulators based on low order finite vol-ume method suffers grid orientation effects when modelingmiscible displacement with adverse mobility ratio. In thistalk, we propose a fully coupled and implicit discontinuousGalerkin (DG) formulation which can accurately computethe flux direction and effectively remove the grid orienta-tion effects. P-adaptive DG scheme will also be proposedso that high order DG is used only at locations where highgradients of concentration are present. Numerical resultsshow that the time spent for p-adaptive scheme is compa-rable to the low order methods.

Hao Huang, Huafei Sun, Aruna Mohan, Jichao YinExxonMobil Upstream Research Companyhao.huang@exxonmobil.com, huafei.sun@exxonmobil.com,aruna.mohan@exxonmobil.com,jichao.yin@exxonmobil.com

Guglielmo ScovazziDuke Universityguglielmo.scovazzi@duke.edu

Co2 Vertical Migration Through a Piecewise Ho-mogeneous Porous Medium

We consider the migration of a CO2 plume through a ver-tical column filled with a piecewise homogeneous porousmedium. The impact of capillary pressure and flux con-tinuities at the interface on the CO2 migration is studiednumerically and mathematically. We analyze how satura-tions and saturation gradients on either side of the inter-face evolve with time and if a local steady state is reached.Different cases are considered : capillary dominant, grav-ity dominant and intermediate case. The influence of thismicro-scale dynamics on upscaled migration is discussed.

Emmanuel MoucheCEA, DRNFranceemmanuel.mouche@cea.fr

Tri Dat NgoCEA, DSM-LSCEtri-dat.ngo@lsce.ipsl.fr

Pascal audiganeBRGM, D3E-SVPpascal.audigane@brgm.fr

Reservoir Modelling Based on Transmissibility Up-scaling

Prediction of reservoir performances requires coarse modelscoherent with fine scale geology. In Eni methodology effec-tive coarse transmissibility (T*) is used in place of perme-ability. This is motivated by the results achieved wheneverT* has been implemented on field models where geologicaland simulation grids are aligned. The issue is to deal withgeometries where coarse and fine grids are misaligned. Inthis work real field applications will show T* benefit on

74 GS13 Abstracts

aligned 3D grids, while the effectiveness on misaligned isproved on 2D synthetic cases.

Paola PanfiliEni E&Ppaola.panfili@eni.com

Alberto CominelliENI E&Pacominelli@eni.com

Luca Turconi, Anna ScottiPolitecnico di Milanolturconi@gmail.com, anna.scotti@mail.polimi.it

On the Impact of Anisotropic Mesh Adaptation onSolute Transport Modeling in Porous Media

We propose an anisotropic mesh adaptation technique formodeling solute transport in porous media. The methodrelies on a recovery-based error estimator and is coupledwith a finite element code solving the Advection Disper-sion Equation. The proposed methodology is assessedagainst experimental breakthrough curves collected in ho-mogeneous and heterogeneous media. We compare resultsobtained by adapting the mesh according to various indica-tors. We analyze the impact of mesh adaptation on optimalparameter estimation for the experiments considered.

Bahman Esfandiar JahromiPhD student at D.I.I.A.R.Hydraulic section, Politecnico di Milanobahman.esfandiar@mail.polimi.it

Alberto GuadagniniLos Almos National Laboratoryalberto.guadagnini@polimi.it

Giovanni PortaD.I.I.A.R., Sezione IdraulicaPolitecnico di Milanogiovanni.porta@polimi.it

Simona PerottoMOX - Modeling and Scientific ComputingDipartimento di Matematicasimona.perotto@polimi.it

Simulating Non-Dilute Transport in Porous MediaUsing a Tcat-Based Model

Predicting the transport of non-dilute species in fluids ofvariable density in porous media is a challenging problemfor which existing models are unable to represent accu-rately the experimental data collected to date. We considerthe displacement of an aqueous phase with dense brine so-lutions. Displacement experiments were conducted in ver-tically oriented 1D columns. Simulation of a non-dilutesystem based upon the thermodynamically constrained av-eraging theory (TCAT) using an entity-based momentumequation was compared to data. The model accounts forthe effects of non-dilute, non-ideal systems and consistsof a nonlinear set of equations including a flow equation,a species transport equation, and closure relations. Werewrite the entity-based model as a system of two cou-pled partial differential-algebraic equations with relevant

closure relations. We use a stiff temporal integrator tocreate 1D simulations of the model. We will discuss bothresults and numerical difficulties.

Deena HannounNorth Carolina State Universitydhannou@ncsu.edu

Structure of Reaction Fronts in Porous Media

Multicomponent reactive flow and transport in permeablemedia gives rise to reaction fronts with complex morphol-ogy. The first-order structure of these patterns can beanalyzed in the hyperbolic limit of the governing equa-tions. Comparisons between analytic solutions, numericalsimulations and field as well as experimental data for ion-exchange reactions shows good agreement. New theoreticalresults for reactive transport with pH-dependent surfacecomplexation reactions show a more complex morphologyof the reaction front and provide the first semi-analyticbenchmarks for numerical simulations of this phenomenon.

A Comparison of Closures for Stochastic Transport

Perturbation-based moment equations for randomly ad-vected solute produce unrealistic multimodality, contraryto macrodispersion theory despite strong similarities be-tween the two. A study of basic macrodispersion ap-proximations reveals higher-order terms that are effectivelyadded to conventional moment-equation approximations atsecond and fourth order. We propose a closed-form approx-imation to two-point (auto)covariance in a manner con-sistent with macrodispersion theory and illustrate its im-provement upon moment-equation approximations for anexample of transport in stratified random media.

Kenneth D. Jarman, Alexandre M. TartakovskyPacific Northwest National Laboratorykj@pnnl.gov, alexandre.tartakovsky@pnl.gov

Large - Time Behavior of the Solution for Nonlin-ear Random Boussinesq - Glover Equation Drivenby Colored Noise

We study the nonlinear random Boussinesq Glover equa-tion in Banach spaces, driven by a colored noise and withrandom initial condition. The noise process is defined asstationary solution of a stochastic differential equation infinite dimensional (or Hilbert) spaces. Under suitable as-sumptions, we prove the existence of stationary solutionand the path wise global attractor. The attractor is P a.s. independent of probabilitary variable. Similar resultsarise in nonlinear random reaction diffusion equations.

Fejzi KolaneciUniversity of New York, Tiranafkolaneci@unyt.edu.al

Multilevel Monte Carlo (MLMC) for Two Phase

GS13 Abstracts 75

Flow and Transport in Random HeterogeneousPorous Media

Monte Carlo (MC) is an established method for quantifyinguncertainty arising in subsurface flow problems. Extend-ing MC by means of multigrid techniques yields the MLMCmethod. In this study, MLMC is applied to assess uncer-tain two phase flow and transport in random heterogeneousporous media. It was found that the computational costsof MLMC are substantially lower compared to MC.

Florian MullerInstitute of Fluid DynamicsETH Zurichflorian.mueller@sam.math.ethz.ch

Patrick JennyInstitute of Fluid DynamicsETH Zurichjenny@ifd.mavt.ethz.ch

Daniel W. MeyerInstitute of Fluid Dynamicsmeyerda@ethz.ch

From Nonlinear Adsorption at Microscale to Non-linear Diffusion at Macroscale.

We have considered the coupled convection-diffusion equa-tions for the bulk and surface concentrations at the mi-croscale of a periodic porous medium. The coupling isthrough a reaction term expressing nonlinear adsorptionphenomena at the solid-fluid interface. Two-scale asymp-totic expansion with drift helps to pass from microscale tomacroscale description. Upscaled equation is a nonlineardiffusion equation. Numerical simulations are done to ap-proximate the solution for the microscale problem usingcorrectors.

Harsha Hutridurga Ramaiah, Gregoire AllaireEcole Polytechniquehutridurga@cmap.polytechnique.fr,allaire@cmap.polytechnique.fr

A Multi-Scale Numerical Simulation of CarbonateRocks Properties Using 3D Micro-Tomography Im-ages

We have estimated the porosity, the permeability and theelastic moduli of fifteen samples from a carbonate reservoirusing numerical simulations on 3D micro-tomography im-ages. Core plugs were scanned at a coarse scale and a fewmillimeters subsets were extracted and digitalized at a finerscale to take into account rock heterogeneity. The compar-ison between simulated and experimental laboratory prop-erties showed a relative good agreement. Advantages andlimitations of the proposed methodology will be discussed.

Mohamed S. JouiniThe Petroleum Institute of Abumjouini@pi.ac.ae

Sandra VegaThe Petroleum Institute of Abu Dhabisvega@pi.ac.ae

A Multi-Scale Method to Include Analytical Solu-tions for Multi-Phase Leakage Through Faults in aNumerical Model

A computationally efficient approach to multi-phase flowmodeling of geologic basins containing faults is developedbased on embedding analytical solutions within coarse-scale numerical models. The analytical solutions are usedto determine the fluxes in and around the fault and thepressure corrections that relate pressure at a given fault tothe coarse-scale pressure in the numerical grid blocks. Thismethod accounts for both vertical and lateral flow withinthe fault.

Mary KangPrinceton Universitymarykang@princeton.edu

Jan M. NordbottenDepartment of MathematicsUniversity of Bergenjan.nordbotten@math.uib.no

Florian DosterDep. of CEE, Princeton UniversityDep. of Mathmatics, University of Bergenfdoster@princeton.edu

Karl BandillaPrinceton Universitybandilla@princeton.edu

Michael A. CeliaPrinceton UniversityDept of Civil Engineeringcelia@princeton.edu

A Multiscale Finite Element Method for TransportModeling

Simulating flows in porous media often requires the reso-lution of convection-diffusion problems where diffusion co-efficient and velocity exhibit strong variations at a muchsmaller scale than the domain of resolution. This work pro-poses a new multiscale finite element method to first solvethis kind of problems on coarse grids and then reconstructthe variations of the solution on a finer grid. An a pri-ori error estimate is established and numerical results arepresented.

Franck Ouaki, Guillaume EncheryIFP Energies nouvellesfranck.ouaki@ifpen.fr, guillaume.enchery@ifpen.fr

Sylvain DesroziersIFP Energies Nouvellessylvain.desroziers@ifpen.fr

Gregoire AllaireCMAP, Ecole Polytechniquegregoire.allaire@polytechnique.fr

A Multi-Scale Approach to Assessing the Hydro-

76 GS13 Abstracts

logical Connectivity of Road and Stream Networks

We study a forested, upland landscape in northeasternUSA to understand the downstream effects of roads onstreams. Previously, only simple metrics have character-ized road-stream connectivity; few studies have examinedscale or quantified effects on channel morphology. Usingnewly-derived proximity and orientation metrics, statisti-cal analyses show proximity to be successful at distinguish-ing among categories of stream geomorphic condition atthe reach scale. These proximity metrics are even morerevealing when reanalyzed at the tributary scale.

Alison PechenickCollege of Engineering & Mathematical SciencesUniversity of VermontAlison.Pechenick@uvm.edu

Donna RizzoSchool of EngineeringUniversity of Vermontdonna.rizzo@uvm.edu

Leslie MorriseyRubenstein School of Environment & Natural ResourcesUniversity of Vermontleslie.morrissey@uvm.edu

Kerrie GarveyThe Rubenstein School of Environment & NaturalResourcesUniversity of Vermontkerrie.garvey@uvm.edu

Kristen UnderwoodSchool of EngineeringUniversity of Vermontkristen.underwood@uvm.edu

Beverley WempleDepartment of GeographyUniversity of Vermontbeverly.wemple@uvm.edu

Adaptative Multi-Scale Parameterization in Frac-tured Porous Media

Flow in fractured porous media is very complex. An in-verse model using a double porosity approach is developedsolving the direct problem with a Quasi-Newton algorithmcoupled with the adjoint-state method to calculate the ob-jective function gradient (OFG). The inverse problem issolved on a reduced number of parameters using an Adap-tative Multi-scale Parameterization with successive meshrefinement depending on the OFG value. The model is vali-dated on the Hydrogeological Experimental Site of Poitiers.

Nicolas TrottierCommissariat a l’Energie AtomiqueLaboratoire d’Hydrologie et de Geochimie de StrasbourgNicolas.TROTTIER@cea.fr

Applications of Level Set Methods in Numerical

Modelling of Flow and Transport Problems

An introductory overview of level set methods and theirapplicability to solve flow and transport problems with in-terfaces will be given. Finite volume discretization of allinvolved partial differential equations will be described thatis very natural for modelling the flow and transport pro-cesses in porous media. Some particular examples will bepresented that shall illustrate a potential of level set meth-ods in general. P. F.: Application of level set method forgroundwater flow with moving boundary. Adv. Wat. Res.,47:56–66, 2012.

Peter FrolkovicDepartment of MathematicsSlovak University of Technologypeter.frolkovic@stuba.sk

A Locally Conservative Eulerian-Lagrangian FiniteVolume Weno Scheme for Hyperbolic Conservation

The object of this talk is to define a locally conserva-tive Eulerian-Lagrangian finite volume scheme with theweighted essentially non-oscillatory property (EL-WENO)for hyperbolic conservation law. This locally conservativemethod has the advantages of both WENO and Eulerian-Lagrangian schemes. It is formally high-order accurate inspace (we present the fifth order version) and essentiallynon-oscillatory. Moreover, it is free of a CFL time step re-striction for linear advection equations, with a relaxed CFLtime step restriction for nonlinear hyperbolic equations andhas small time truncation error. A subcell WENO recon-struction procedure is defined, and this procedure makesit possible for this Eulerian-Lagrangian schemes. Flux cor-rections are carried out over the approximated characteris-tic lines using the Runge-Kutta method with natural con-tinuous extension scheme. Numerical results are providedto illustrate the performance of the scheme.

Chieh-Sen Huangational Sun Yat-sen UniversityKaohsiung, Taiwanhuangcs@math.nsysu.edu.tw

A Locking-Free Lowest-Order Discretization ofBiot’s Consolidation Model on General Meshes

We present an original Euler-Gradient Scheme discretiza-tion (i.e. implicit Euler in time and Gradient Scheme inspace) of Biot’s consolidation model on general meshes.Gradient Schemes are a generic framework which encom-passes a large class of nonconforming methods such as theHybrid Finite Volumes. Under sufficient conditions on thespace discretization, and under minimal regularity assump-tions on the solution, we prove the convergence of thisgeneric scheme on general meshes. The discretization isalso proved to be locking-free, in the sense that a discreteinf-sup condition guarantees the absence of spurious spa-tial oscillations on the pore pressure in the first time stepsin poorly permeable regions.

Simon Lemaire

GS13 Abstracts 77

IFP Energies nouvellessimon.lemaire@ifpen.fr

Daniele Di PietroUniversity Montpellier 2I3M - ACSIOMdaniele.di-pietro@univ-montp2.fr

Robert EymardUniversity Paris Eastrobert.eymard@univ-mlv.fr

Space-Time Hybridizable Discontinuous GalerkinMethods for Incompressible Flows

I will discuss a new Discontinuous Galerkin (DG) method,namely the Hybridizable DG (HDG) method. We recentlyextended the HDG method to a space-time formulationallowing efficient and accurate computations on deform-ing grids/domains. I will introduce the method for theIncompressible Navier-Stokes (INS) equations. A compari-son of results and efficiency will then be made between thespace-time HDG and DG method for the INS equations ondeforming domains.

Sander RhebergenUniversity of MinnesotaSchool of MathematicsSander.Rhebergen@earth.ox.ac.uk

Bernardo CockburnSchool of MathematicsUniversity of Minnesotacockburn@math.umn.edu

Jaap van Der VegtUniversity of Twentej.j.w.vandervegt@utwente.nl

A Cell-Centered Scheme for the Heterogeneousand Anisotropic Diffusion Equations on DistortedMeshes

In this paper, we derive a finite volume scheme for theheterogeneous and anisotropic diffusion equations on gen-eral, possibly nonconforming meshes. This scheme hasboth cell-centered unknowns and vertex unknowns. Thevertex unknowns are treated as intermediate ones and areexpressed as a linear combination of the neighboring cell-centered unknowns, which reduces the scheme to a com-pletely cell-centered one. The coefficients in the linearcombination are known as the weights and two types ofnew explicit weights are proposed, which allow arbitrarydiffusion tensors, and are neither discontinuity dependentnor mesh topology dependent. These new weights can re-duce to the one-dimensional harmonic-average weights onthe nonuniform rectangular meshes, and moreover, are eas-ily extended to the unstructured polygonal meshes andnon-matching meshes. Both the derivation of the nine-point scheme and that of new weights satisfy the linear-ity preserving criterion which requires that a discretizationscheme should be exact on linear solutions. Numerical ex-periments show that, with these new weights, the resultingnew scheme and its simple extension maintain optimal con-vergence rates for the solution and flux on general polyg-onal distorted meshes in case that the diffusion tensor is

taken to be anisotropic, at times heterogenerous, and/ordiscontinuous.

Qiang ZhaoInstitute of Applied Physics and ComputationalMathematicsBeijing,P.R.ChinaQ.ZHAO.CN@gmail.com

Xia CuiInstitute of Applied Physics and ComputationalMathematicsLaboratory of Computatinal Physics,Beijing,P.R.Chinacuixia09@gmail.com

Guangwei YuanInstitute of Applied Physics and ComputationalMathematicsLaboratory of Computational Physicsygw8009@sina.com

In Search for a Robust Representation of Cloud Mi-crophysics for Aerosol-Cloud-Aerosol Interactions

Representation of such processes as cloud drops formationon aerosol particles and further processing of the aerosolphysicochemical properties by precipitation-forming cloudsrepresents a challenge for classical bulk, multi-moment andbin models of cloud microphysics. Several alternative ap-proaches have been recently proposed such as Lagrangianparticle-tracking simulations or multi-dimensional bin ap-proaches. In this study we intercompare these novelschemes using a 2-dimensional prescribed-flow simulationsof drizzling marine stratocumulus to systematically analyzethe mechanisms by which the physiochemical properties ofaerosols change in warm clouds.

Sylwester J. ArabasInstitute of Geophysics, Faculty of PhysicsUniversity of Warsaw, Polandsarabas@igf.fuw.edu.pl

Miroslaw AndrejczukDepartment of Physics, University of Oxford, UKandrejczuk@atm.ox.ac.uk

Wojciech GrabowskiNational Center for Atmospheric Research, Boulder,Coloradograbow@ucar.edu

Anna JarugaInstitute of Geophysics, Faculty of PhysicsUniversity of Warsaw, Polandajaruga@igf.fuw.edu.pl

Zachary LeboNational Center for Atmospheric Research, Boulder,Coloradolebo@ucar.edu

Hanna PawlowskaInstitute of Geophysics, Faculty of PhysicsUniversity of Warsaw, Polandhanna.pawlowska@igf.fuw.edu.pl

78 GS13 Abstracts

Asymptotic Modeling ofNon-Hydrostatic/Hydrostatic Dynamical Couplingin the Ocean Surface Boundary Layer

A primary challenge in physical oceanography is the sys-tematic representation of non-hydrostatic boundary-layer(BL) turbulence in numerical models and stability analysesof hydrostatic flows. Here, we use asymptotic analysis toderive a multiscale PDE model that captures the couplingbetween wind-driven Langmuir turbulence and O(10)-kmsubmesoscale flows in the ocean surface BL. Numerical sim-ulations and nonlinear WKBJ analysis confirm that non-hydrostatic/hydrostatic coupling gives rise to a variety ofnovel upper ocean phenomena.

Greg ChiniProgram in Integrated Applied MathematicsUniversity of New Hampshiregreg.chini@unh.edu

Ziemowit MalechaUniversity of New HampshireProgram in Integrated Applied Mathematicszmy4@unh.edu

Zhexuan ZhangUniversity of New HampshireDepartment of Mechanical Engineeringzrg2@unh.edu

Keith JulienApplied MathematicsUniversity of Colorado, Boulderkeith.julien@colorado.edu

Weather Models of Anomalous Diffusion

The numerical simulation of fractional diffusion equationsin three dimensions is considered, to describe fluid flowthrough porous media. A fractional version of the Alter-nating Direction Implicit (ADI) scheme is proposed. Astrategy improving the speed of convergence by an extrap-olation method is also presented. Numerical results aregiven to support our theoretical analysis.Keywords: anomalous diffusion; fractional diffusion, frac-tional partial derivatives; Alternating Direction Implicit(ADI) scheme; extrapolation techniques.

Moreno ConcezziUniversity of Roma Tremoreno.concezzi@hotmail.it

Water in the Subducting Oceanic Plate: a Trilogy

In this presentation we summarize the results of a projectfocused on geological processes related to water in the slabat different stages of subduction. We discuss numericalmodeling results of fluid flow during slab hydration anddehydration, potential geophysical implications of an hy-drated slab at intermediate-depths and deep subduction offluids.

Manuele FaccendaDipartimento di GeoscienzeUniversita di Padovamanuele.faccenda@gmail.com

Luigi BurliniInsittue of Geoscience, ETH Zurichluigi.burlini@erdw.ethz.ch

Taras GeryaGeophysical InstituteETH-Zurichtaras.gerya@erdw.ethz.ch

Neil MancktelowInsittue of Geoscience, ETH Zurichneil.mancktelow@erdw.ethz.ch

A Non-Hydrostatic Spectral-Element Model of theAtmosphere

To perform climate simulations at resolutions greater than1/8th of a degree, the hydrostatic primitive-equations mustbe replaced with non-hydrostatic Euler equations valid inthis regime. To this end, we are working to develop anon-hydrostatic version of CAM-SE, the spectral-elementCommunity Atmosphere Model used at NCAR. We willdiscuss the design choices made in the new non-hydrostaticdynamical core and present some preliminary results.

David M. HallUniversity of Colorado at BoulderDepartment of Computer Sciencedavid.hall@colorado.edu

Perfectly Matched Layers for the Wave Equationin Discontinuous Media

Applications arising in geophysics and electromagneticproblems can be composed of layers of rock, water and pos-sibly oil. The ultimate goal of this project is to investigatethe efficiency of the PML in a layered media. We considera computational set-up consisting of smaller structured do-mains that are patched together to a global domain, usinghigh order difference operators for approximating spatialderivatives and weak enforcements of interface conditions.Numerical simulations will be presented demonstrating thestability and high order accuracy of our schemes.

Kenneth DuruDivision of Scientific ComputingUppsala Universitykduru@stanford.edu

Numerical Approximation for a Model of MethaneHydrates

We consider a simplied model for evolution of methanehydrates in the hydrate zone, which includes a parameter-dependent maximum solubility constraint represented as anonlinear complementarity constraint (for solubility). Ourmodel consists of a single PDE and two unknowns (sol-ubility and saturation) which are bound by a parameterdependent family of graphs. We analyze solvability andother properties of the fully discrete scheme for the model,and discuss current extensions.

F. Patricia MedinaDepartment of MathematicsOregon State University

GS13 Abstracts 79

medinaf@math.oregonstate.edu

Nathan L. GibsonOregon State Universitygibsonn@math.oregonstate.edu

Malgorzata PeszynskaDepartment of MathematicsOregon State Universitympesz@math.oregonstate.edu

Ralph E. ShowalterOregon State Universityshow@math.oregonstate.edu

Fast Uncertainty Quantification of Subsurface Flowand Transport with Markovian Velocity Processes

Contaminant transport predictions in large subsurface sys-tems involve high uncertainties due to sparse conductivitymeasurements. To quantify these uncertainties, we proposea simulation method that is about three orders of magni-tude faster than conventional Monte Carlo simulation. Thenew method is based on parameterized Markov processesfor the velocity of fluid particles, which allow for the pres-ence of an arbitrary number of conductivity measurements.

Daniel W. MeyerInstitute of Fluid Dynamicsmeyerda@ethz.ch

A Bioventing Mathematical Model Based on PureOxygen Injection

A mathematical model and the simulation of subsoil decon-tamination by bioventing will be presented. The bases forthe model construction are the following: (1) the pollutantis considered as immobile and confined in the unsaturatedzone; (2) only oxygen is injected in the subsoil by wells;(3) the bacteria acting the pollutant removal are immobileand their growth depends on oxygen and pollutant concen-tration.

Filippo NotarnicolaIstituto Applicazioni Calcolo, I.A.C. - CNR, Barif.notarnicola@ba.iac.cnr.it

Torsional Wave Dispersion Relation in a Self-Reinforced Layer over a Gravitating ViscoelasticHalf Space

The present paper constitute the study of torsional surfacewave propagation in a self-reinforced layer resting over agravitating viscoelastic half space. The layer has an inho-

mogeneity of linear type associated with the rigidity anddensity of the medium. Dispersion equation has been ob-tained in the terms of HypergeometricU and LaugurreLfunction. The dispersion equation reduces to a classicalform as a particular case. The influence of various pa-rameters has been depicted by means of graphs for bothreinforced and reinforcement free medium.

Sumit K. Vishwakarma, Shishir GuptaIndian School of Mines, Dhanbad, Jharkhand,India-826004sumo.ism@gmail.com, shishir ism@yahoo.com

A Fourier Finite Element Method for the Simula-tion of 3D Csem Measurements

We present a novel numerical method to simulate 3D geo-physical controlled source electromagnetic (CSEM) mea-surements. The method combines a 2D finite elementmethod (FEM) in two spatial dimensions with a hybriddiscretization based on a Fourier-FEM along the third spa-tial dimension. The method delivers high accuracy simu-lations of marine CSEM problems with arbitrary 3D ge-ometries while it considerably reduces the computationalcomplexity of traditional 3D simulators, since Fourier basisfunctions are mutually orthogonal within the backgroundlayers.

Shaaban A. BakrSenior Researcher, Uni CIPR, P.O. Box 7810, N-5020Bergen,Norwayshaaban.bakr@uni.no

David PardoDepartment of Applied Mathematics, Statistics, andOperational Research, University of the Basque Countrydzubiaur@gmail.com

Trond MannsethCentre for Integrated Petroleum ResearchUniversity of Bergen, Norwaytrond.mannseth@uni.no

Expected Value Estimators in Nuclear Well-Logging Simulations

Simulation of nuclear well-logging tools and their responsesis a long-standing problem, usually solved in the frameworkof transport theory by Monte-Carlo methods. Widely usedconventional Monte Carlo algorithms are often unaccept-able, and variance reduction techniques are required. Inthis talk, the algorithms with expected value estimators areconsidered. These algorithms showed their efficiency whenapplied to different types of nuclear well-logging problems.The description and analysis of the results are the subjectsof the presentation.

Bair BanzarovBaker Hughes Inc.bair.banzarov@bakerhughes.com

Seismic Stratigraphic Modelling Through Comput-

80 GS13 Abstracts

ing in Bengal Basin at Higher Depths

Stratigraphic seismic modelling through software packageSTICHA between two wells of Bengal Basin at differentdepths between 2000ft to 4400 ft,the zone of interest forcrude oil bearing, has been made and analysis has beenmade geologically for potential oil-bearing.The Depth mod-els and respective synthetic seismic setion models at differ-ent interesting layers have been developed. The resultsmatch comfortably .The drilling data agrees with seismicmodels made.This is economic in oil exploration.

Dr Sisir Kumar BhowmickGMIT,Balarampur,BaruipurKolkata-700144sisirkr@rediffmail.com

Inexact Interior Point Algorithms for SeismicImaging

An inexact interior-point algorithm is devised and its per-formance is compared against the exact one on severallinear and nonlinear PDE-constrained optimization prob-lems. Schur-complement preconditioners for the resultingKKT systems are constructed and their robustness is in-vestigated for every benchmark problem considered. Ap-plication areas include parameter estimation in diffusionproblems, super-conductivity and seismic imaging both inthe frequency and time domains.

Drosos KourounisUSI - Universita della Svizzera italianadrosos.kourounis@usi.ch

Johannes HuberUniversitat BaselDepartment of Mathematicsjohannes.huber@unibas.ch

Marcus J. GroteUniversitat Baselmarcus.grote@unibas.ch

Olaf SchenkUSI - Universita della Svizzera italianaolaf.schenk@usi.ch

Mathematical Techniques for Very Large Scale To-mographic Inversion

We present an approach to find regularized solutions tovery large linear systems arising from a tomographic in-verse problem that are difficult to handle directly even withlarge computational resources. We present a system usingmatrices that reach terabytes in size. We use a multi-stepapproach to work with such systems, consisting of waveletcompression and randomized low rank SVD approxima-tions. We obtain significant reductions in size and speed-upin computation time.

Sergey VoroninPrinceton Universityvoronin@geoazur.unice.fr

Guust Nolet, Dylan Mikesell, Jean CharletyUniversite de Nice Sophia-AntipolisCNRS, Obs. de la Cote d’Azur, Geoazur

nolet@geoazur.unice.fr, dmikesell@geoazur.unice.fr,charlety@geoazur.unice.fr

Gradient-Based Techniques for Data Assimilationin Reservoir Simulation

A computational framework that combines a full-featuredcompositional reservoir simulator with adjoint-based in-verse modeling is presented. Automatic differentiation isapplied to facilitate construction of the required deriva-tives. The spatial correlation structure of the geologicalmodel is captured using a PCA-based regularization, withthe PCA basis determined from geostatistical modeling. Anew zonation procedure based on sensitivity magnitude isintroduced. History matching results using the new frame-work are presented for challenging problems.

Vladislav Bukshtynov, Oleg Volkov, Lou J. DurlofskyStanford Universitybukshtu@stanford.edu, ovolkov@stanford.edu,lou@stanford.edu

Khalid AzizStanford UniversityDepartment of Energy Resources Engineeringaziz@stanford.edu

Polymer Injection Optimization Using the Ensem-ble Kalman Filter

Eni is currently studying the applicability of polymer-basedEOR to brown fields. A workflow hinged on the EnsembleKalman filter (EnKF) has been developed to assimilateproduction data, evaluate the efficiency of the polymer,quantify process-relevant uncertainties and maximize theeconomical revenue. In this work, EnKF is used to generatean ensemble of history matched models for a field sector,with careful estimation of the boundary condition. Then,the ensemble logic is used for a robust optimisation of theeconomic return of the EOR project.

Laura Dovera, Stefano Raniolo, Alberto Cominelli,Chiara Callegaro, Franco MasseranoENI E&Plaura.dovera@eni.com, stefano.raniolo@eni.com,acominelli@eni.com, chiara.callegaro@eni.com,franco.masserano@eni.com

Dual States Estimation Using Ensemble KalmanFiltering for Subsurface Flow-Transport CoupledModels

Modeling contaminant evolution in geologic aquifers re-quires coupling a groundwater flow model with a contam-inant transport model. Assuming perfect flow, an ensem-ble Kalman filter can be directly applied on the transportmodel but this is very crude assumption as flow modelscan be subject to many sources of uncertainties. If theflow is not accurately simulated, contaminant predictionswill likely be inaccurate even after successive Kalman up-dates of the contaminant with the data. In this study, wepropose a dual strategy for this one way coupled system bytreating the flow and the contaminant models separatelywhile intertwining a pair of distinct Kalman filters; oneon each model. Preliminary results suggest that on top

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of simplifying the implementation of the filtering system,the dual approach provide time consistent updating schemeand more stable and accurate solutions than the standardjoint approach.

Mohamad El GharamtiKing Abdullah University of Science and Technologymohamad.elgharamti@kaust.edu.sa

Ibrahim HoteitKing Abdullah University of Science and Technology(KAUST)ibrahim.hoteit@kaust.edu.sa

Johan ValstarDeltares - Utrecht, Netherlandsjohan.valstar@deltares.nl

Geodetical Data Assimilation with EnsembleKalman Filter

Geomechanical phenomena are fundamental in explainingthe dynamic behaviour of the reservoir: surface displace-ments measurements can provide additional insight intothe nature of the reservoir rock and help constrain thereservoir model. In this study, an integrated workflow forthe assimilation of dynamic flow measure data and surfacedisplacements observations has been developed through theEnsemble Kalman Filter approach, in order to estimatereservoir flow and material properties and to identify com-partments not yet drained.

Silvia Monaco, Francesca Bottazzi, Marco Sciortino,Laura DoveraENI E&Psilvia.monaco@eni.com, francesca.bottazzi@eni.com,marco.sciortino@eni.com, laura.dovera@eni.com

Impact of Model Order Reduction to HydrologicalData Assimilation.

Sophisticated data assimilation (DA) techniques, e.g. par-ticle filters with MCMC, have been recently developed toaddress inverse problems. These methods are difficult toapply to high-dimensional models, since they require manysystem solutions. Reduced order models (RM) reduce thecomputational burden required to solve transient PDEs.Here we investigate the application of DA schemes with alarge number of realizations computed with the RM. Ourpreliminary results show that DA techniques correct theRM errors.

Damiano Pasetto, Mario PuttiUniversita di Padovadamiano.pasetto@ete.inrs.ca, putti@dmsa.unipd.it

William W-G. YehUniversity of California,Los Angeleswilliamy@seas.ucla.edu

Improved Estimation of the Stochastic Gradientwith Quasi-Monte Carlo Methods

Stochastic approximation of the gradient, although not as

efficient as adjoints, has recently received significant at-tention for solution of optimization problems where ad-joints are not available or difficult to implement. Thesemethods are generally much easier to implement as theyare non-intrusive and treat the simulator as a black box.In this work, we propose the application of quasi-MonteCarlo methods for improving the efficiency and accuracyof the stochastic gradient compared to current methods.While the existing approaches rely on Monte Carlo sam-pling, quasi-Monte Carlo sampling has a better conver-gence rate leading to more accurate and efficient gradi-ent approximation. In particular, we apply the Sobol se-quence for sampling, which demonstrates better conver-gence compared to other quasi-Monte Carlo sampling tech-niques. More than 30% improvement was obtained in theaccuracy of the stochastic gradient calculated with Sobolsampling over standard Monte Carlo sampling.

Pallav SarmaChevron Energy Technology CompanySan Ramon CApallav@chevron.com

Wen ChenChevron ETCwhch@chevron.com

Subglacial Water Flow Beneath Ice Streams

Ice streams, characterised by high basal sliding velocities,play a dominant role in ice sheet drainage. Subglacial hy-drology is believed to be one of the main controlling fac-tors in their spatial and temporal evolution: how the waterdrains beneath an ice sheet has important implications forthe ice-bed boundary condition. We pose a model to de-scribe subglacial stream flow through the underlying sed-iment, and consider the coupled behaviour of the ice andmeltwater systems.

Teresa M. Kyrke-SmithUniversity of Oxfordteresa.kyrke-smith@earth.ox.ac.uk

Towards a New Marine Ice-Sheet Model

We present a unified model in order to model an ice flow.The grounded part (ice sheet and ice shelf) leads to aunique lubrication-type model. A new model for the float-ing ice mass is developed. We consider the ice shelf as atwo free surface problem with a lateral sea pressure force atcalving front. We obtain an integro-differential evolutionequation of the ice shelf thickness.

Marc Boutounet, Jerome MonnierInstitut de Mathematiques de ToulouseINSA dpt GMMboutoune@insa-toulouse.fr,jerome.monnier@insa-toulouse.fr

Control Method Inversions for Ice Stream BedConditions Using a Higher-Order Glacier Model

Ice streams undergo drag from sliding over their beds, butthis stress is not measurable remotely. However, one canuse observed ice velocities to invert a glacier model for the

82 GS13 Abstracts

spatially-varying bed friction. In this talk, I will comparethe results of inverting two different models from observa-tions at Pine Island Glacier: the shelfy stream equationsand the more complex L1L2 equations. These models aredepth-averaged perturbations of the 3D Stokes equations.

Daniel ShaperoUniversity of Washingtonshapero@uw.edu

A Conceptual Model for Permafrost-Climate Feed-back.

The permafrost methane emission problem is the focusof attention in different climate models. As a result oftundra permafrost thawing, a number of small lakes haveformed and extended, and methane has entered the atmo-sphere. In turn, atmosphere methane can reinforce warm-ing, and there appears to be a positive feedback loop thatcan lead to a climate catastrophe. Mathematically, per-mafrost thawing can be described by the classical Stefanapproach. From this assumption we obtain a determinis-tic equation that serves as an extremely simplified modelfor lake growth. This equation are improved and trans-formed to a more realistic model for estimation of positivepermafrost-climate feedback.

Ivan A. SudakovUniversity of UtahMathematics Departmentsudakov@math.utah.edu

Sergey VakulenkoInstitute for Mechanical Engineering ProblemsRussian Academy of Sciencesvakulenfr@mail.ru

Scale-Aware Parametrization of Eddy Transport

Mesoscale eddies are most energetic in the ocean, and areresponsible for a significant portion of the tracer transport.Multi-resolution ocean models require eddy parametriza-tion schemes that can scale across a wide range of lengthscales existing on the grids. This talk present results froma recent project in designing scale-aware eddy parametriza-tion schemes, which includes a scale-aware generalizationof the anticipated potential vorticity method, the Gent-McWilliams closure with spatially-varying coefficients, andsome ideas for moving forward.

Qingshan ChenFlorida State Universityqchen@lanl.gov

Approximate Deconvolution for Large-Eddy Simu-lation (LES) of the Atmospheric Boundary Layer(ABL) on Adaptive Grids

Simulating the ABL in complex terrain (such as cities)could be faster and more accurate using LES and adap-tive grids. However, combining these techniques generateserrors. Inaccuracies in subfilter models limit LES solutionreliability at the grid scale, contaminating the interpolatedsolution at grid interfaces. The grid interface also reflectshigh wavenumber solution components. We test approxi-

mate deconvolution to mitigate these errors. Results froma flat boundary layer with one grid refinement interface arepresented.

Lauren GoodfriendUC Berkeleylgoodfriend@berkeley.edu

Fotini K. ChowUniversity of California, Berkeleytinakc@berkeley.edu

Marcos Vanella, Elias BalarasGeorge Washington Universitymvanella@gwu.edu, balaras@gwu.edu

Hypothesizing and Testing Causal Relationships inCorrelated Time-Series Observations

Biogeochemical archives record time progression of envi-ronmental conditions. Co-varying measurements enticecause-effect explanations, but establishing causal relation-ships requires rigorous epistemology. Correlation is neces-sary for hypothesizing causation, but insufficient for form-ing conclusions. Amplitude and phase response over fre-quency tests cause-effect scenarios: measured cause mustprecede proportionate effect consistent with direct forcingtheory. Signal coherence offers methods for quantifyingprobabilistic confidence in cause-effect hypotheses. Meth-ods are applied to ice core proxies of temperature and car-bon dioxide concentration.

Gary B. HughesCalifornia Polytechnic State University San Luis Obispogbhughes@calpoly.edu

Asymptotic Approaches for Rotationally Con-strained Flows

Geostrophy, the dominant force balance between the Cori-olis and pressure gradient forces, is often the prevailing fea-ture observed in the convective dynamics of atmospheresand oceans and planetary interiors. The presence of fast in-ertial waves and thin momentum boundary layers pose sig-nificant challenges for direct numerical simulations. In thistalk, I will demonstrate how multiscale asymptotic meth-ods can be utilized to derive reduced PDEs that overcomethese restrictions. Simulations reveal new flow regimes thatremain inaccessible DNS of the Navier-Stokes equations.

Keith A. JulienDepartment of Applied MathematicsUniversity of Colorado at Boulderjulien@colorado.edu

A Stochastic Hydrodynamic Model for BiogenicMixing

As fish or other bodies move through a fluid, they stir theirsurroundings. This can be beneficial to some fish, since theplankton they eat depends on a well-stirred medium to feedon nutrients. Bacterial colonies also stir their environment,and this is even more crucial for them since at small scalesthere is no turbulence to help mixing. It has even beensuggested that the total biomass in the ocean makes a sig-

GS13 Abstracts 83

nificant contribution to large-scale vertical transport, butthis is still a contentious issue. We propose a simple modelof the stirring action of moving bodies through both invis-cid and viscous fluids. In the dilute limit, this model canbe solved using Einstein and Taylor’s formula for diffusion(Brownian motion). We compare to direct numerical simu-lations of objects moving through a fluid. This is joint workwith Jean-Luc Thiffeault (Wisconsin) and Steve Childress(NYU).

Zhi George LinZhejiang Universitylinzhi80@zju.edu.cn

A Thermostat Approach to Correction of KineticEnergy Spectra

Numerical simulations of atmospheric flows typically useartificial viscosity to avoid spectral blocking. This disruptsthe vorticity cascade and suppresses the growth of distur-bances. We introduce a thermostat to correct the spectrumby adding a small stochastic perturbation to each mode ina spectral truncation. In Burgers’ equation this approachyields the correct energy spectrum with mild perturbationof dynamics. We also discuss prospects for application totwo-dimensional flow.

Keith MyerscoughDelft University of Technologykeith@cwi.nl

Jason FrankCentrum Wiskunde & Informaticajason@cwi.nl

Benedict LeimkuhlerUniversity of Edinburghb.leimkuhler@ed.ac.uk

Goal-Oriented Adaptive Meshing for the ShallowWater Equations

The dual-weighted residual method provides an error esti-mator which can be used as a mesh refinement criterion foradaptive methods. By utilization of the adjoint, the DWRmethod takes the discretization error of the scheme andalso user specified quantities of interest into account. Wetested the DWRmethod with a discontinuous Galerkin dis-cretization of the shallow water equations. Our test prob-lem is a 2D storm track simulation which is sensitive to thegrid refinement.

Susanne BeckersKlimaCampus, Universitat Hamburgsusanne.beckers@zmaw.de

Jorn BehrensKlimaCampus, University of Hamburgjoern.behrens@zmaw.de

Winnifried WollnerUniversity of Hamburg, Department of Mathematicswinnifried.wollner@math.uni-hamburg.de

Central-Upwind Schemes for the System of Shal-

low Water Equations with Horizontal TemperatureGradients

We consider a modification of the Saint-Venant system ofshallow water equations. The studied model, proposed byRipa, takes into account temperature variations, which ef-fect the pressure term while the temperature is transportedby the fluid, which makes the model substantially morecomplicated than the classical Saint-Venant system. We in-troduce a central-upwind scheme for the Ripa system. Thescheme is well-balanced, positivity preserving and does notdevelop spurious pressure oscillations across temperaturejumps. Such oscillations would typically appear when con-ventional Godunov-type methods are applied to the Ripasystem, and the nature of the oscillation is similar to theones appearing at material interfaces in compressible mul-tifluid computations. The resulting scheme is highly ac-curate, preserves two types of lake at rest steady states,and is oscillation free across the temperature jumps, as itis illustrated in a number of numerical experiments.

Alina ChertockNorth Carolina State UniversityDepartment of Mathematicschertock@math.ncsu.edu

Alexander KurganovTulane UniversityDepartment of Mathematicskurganov@math.tulane.edu

Yu LiuTulane UniversityMathematics Departmentyliu3@tulane.edu

Robust Code-to-Code Validation by Means of Pa-rameter Uncertainty Propagation and Anova

We consider the issue of robust code-to-code validation forlong wave run-up on complex bathymetries. The objectiveis the assessment of the output sensitivity w.r.t. modelparameters affecting the properties of the schemes. We willcompare the behavior of two shallow water codes using thesecond order scheme of Nikolos and Delis (CMAME 1982009) and of Ricchiuto (AIP Proc. 1389 2011). Robustvalidation is achieved by using uncertainty propagation andanalysis of variance to compare the codes single parametersensitivities.

Pietro M. Congedo

INRIA Bordeaux Sud-Ouest (FRANCE)pietro.congedo@inria.fr

Anargyros DelisTechnical University of Creteadelis@science.tuc.gr

Mario RicchiutoINRIAmario.ricchiuto@inria.fr

Shallow Water Simulations with the Source Termby the Depth Gradient and Weighted Average Flux

84 GS13 Abstracts

Methods

A finite volume scheme based on depth gradient method(DGM) and weighted average flux (WAF) method withsource term has been formulated to solve the two-dimensional shallow water equations. Approximated so-lutions are updated in time using predictor-corrector typesof methods. The predictor step is calculated by the DGMwith piecewise-linear reconstructions in each cell volume.Computations at the corrector step are performed usinga total variation diminishing (TVD) variant of the WAFmethod. The accuracy of numerical solutions is demon-strated by applying it to variety of benchmark problems.It is shown that the method is accurate and robust. Also,it can be used to solve problems involving shock-capturing.

Lanchakorn KittiratanawasinDepartment of mathematics, Faculty of ScienceKasetsart Universityfscilkk@ku.ac.th

Anand PardhananiDepartment of Mathematics, Natural Sciences DivisionEarlham College, U.S.A.pardhan@earlham.edu

Montri MaleewongDepartment of mathematics, Faculty of ScienceKasetsart University, Bangkok, Thailandfscimtm@ku.ac.th

Central-Upwind Schemes for Shallow Water Mod-els

The talk will be focused on recent applications of the finite-volume central-upwind schemes to several shallow watermodels including the two-layer shallow water equations,the Savage-Hutter type model of submarine landslides andgenerated tsunami waves, and the non-hydrostatic Saint-Venant system. The main advantages of the central-upwind schemes are their simplicity and robustness, theirability to preserve a delicate balance between the fluxes,(possibly singular) geometric source term and frictionterms as well as to preserve positivity of the computedwater depth.

Alexander KurganovTulane UniversityDepartment of Mathematicskurganov@math.tulane.edu

Total Least-Squares Adjustment for Various Formsof Coordinate Transformations: A Comparison

In recent years, the Total Least-Squares adjustment withinErrors-In-Variables models has been used frequently whenestimating parameters of certain coordinate transforma-tions from empirical data. While the affine-transformationparameters could be solved efficiently in a multivariatesetting, the similarity transformation required algorithmsfor general weight matrices to reflect its special struc-ture. Here, an attempt will be made to develop a unifyingframework that also will allow the treatment of intermedi-ate forms, such as the prototypical “orthogonal coordinate

transformation.’

Burkhard Schaffrin, Kyle SnowSchool of Earth SciencesThe Ohio State Universityaschaffrin@earthlink.net, snow.55@osu.edu

Frank NeitzelDept. of Geodesy and Geoinformation ScienceBerlin University of Technologyfrank.neitzel@tu-berlin.de

A Numerical Approach to Fluid Induced SedimentProcesses

Fluvial bedforms like dunes, ripples or scour marks areformed by current driven sediment transport processes.This includes the interaction of entrainment and depositionof sediment particles. In this study we use a numerical sim-ulation of the three dimensional fluid flow and the simul-taneous transport to reproduce these processes. To solvethe incompressible two-phase Navier-Stokes equations weuse NaSt3D as three dimensional fluid solver for incom-pressible flow problems. High order schemes are appliedfor spatial as well as for temporal discretization. The mainvariants of sediment transport are modelled by applying naadvection-diffusion equation for suspension load and Exnerequation to bed load transport. The rearrangement of sed-iment leads to a new sediment surface height which resultsin new bedforms. To test our model we simulate the evo-lution of a scour mark around an obstacle and the erosionof sediment from a dune crest.

Markus BurkowInstitute for Numerical Simulation, University Bonnburkow@ins.uni-bonn.de

Michael GriebelInstitute for Numerical SimulationUniversity of Bonncontact@ins.uni-bonn.de

Numerical Modeling of Flow Over Flexible Vegeta-tion

The existence of vegetation in a region can greatly increasethe resistance to flow. The vegetation is often highly flexi-ble and moves as the flow field changes which complicatesquantifying the resistance and incorporating it into a flowmodel. We present a method to model resistance due tobending vegetation using the immersed boundary methodfor fluid-structure interaction. Comparisons to several ex-perimental benchmark problems are shown.

Steven A. MattisThe Institute for Computational Engineering and SciencesUniversity of Texas at Austinsteven@ices.utexas.edu

Christopher Kees, Matthew FarthingUS Army Engineer Research and Development Centerchristopher.e.kees@usace.army.mil,

GS13 Abstracts 85

matthew.w.farthing@usace.army.mil

A Residual Based Approach for the Madsen andSorensen Boussinesq Model

We consider the discretization of the Boussinesq modelof Madsen and Sorensen using a residual based ap-proach. Following previous work of Ricchiuto and Boller-man (J.Comput.Phys 228, 2009), we write discrete nodalequations as weighted averages cell residuals obtainedby integrating the time-discretized Madsen and Sorensenequations over a cell. We will discuss the influence ofvarious discretization choices (weights, time discretizationetc.) on dispersion and accuracy properties of the result-ing scheme, and show results on relevant nonlinear wavepropagation and transformation tests.

Mario RicchiutoINRIAmario.ricchiuto@inria.fr

Andrea FilippiniInriaandrea.filippini@inria.fr

Pebble Shape Evolution Along the Williams River,Australia: a Numerical Abrasion Model

Modeling sediment transport and abrasion in various en-vironments is a long-standing problem in sedimentology.We present a new numerical abrasion model describing thecollective evolution of size and shape in large pebble col-lections as a Markov process, due to mutual abrasion andfriction. We apply the model to the Williams River in or-der to reconstruct the downstream variation in grain sizeand shape.

Tımea SzaboDepartment of Mechanics, Materials and StructuresBudapest University of Technology and Economicstszabo@szt.bme.hu

Stephen FityusCentre for Geotechnical and Materials ModellingThe University of Newcastle, Australiastephen.fityus@newcastle.edu.au

Gabor DomokosDepartment of Mechanics, Materials and StructuresBudapest University of Technology and Economicsdomokos@iit.bme.hu

Interval Output of a SISO Linear System withKnown Impulse Response for Incompletely De-scribed Input

In hydrology convolutions are used in the context of hydro-graphs and tracer hydrology. They represent the action of alinear system on an input. Usually the impulse response isa parametrized function and only a time series of averagesof the input is available. For input that is non-negativeand has an essential supremum we apply interval analysisto construct upper and lower bounds for the convolution.

Ronald R. Van Nooijen

Delft University of Technologyr.r.p.vannooyen@tudelft.nl

Alla KolechkinaAronwisa.g.kolechkina@tudelft.nl

Incorporating Tidal Uncertainty Into ProbabilisticTsunami Hazard Assessment (ptha)

We describe two new methods for incorporating tidal un-certainty into the probabilistic analysis of tsunami hazardassessment. These methods couple inundation informa-tion from multiple GeoClaw simulations with tidal patternsfrom the site of interest. Performance of the methods fora recent Crescent City, California study will be illustrated,and advantages over existing methods will be given.

Loyce AdamsUniversity of WashingtonDepartment of Applied Mathematicsadams@amath.washington.edu

Randall J. LeVequeUniversity of Washingtonrjl@uw.edu

FRANK I. GonzalezDept. of Earth and Space SciencesUniversity of Washingtonfigonzal@uw.edu

Strongly Nonlinear Internal Wave Models for TwoLayer Fluids

We present a generalized class of strongly nonlinear inter-nal long wave models in a two-fluid layer system. Keysteps in the derivation of models tailored for different sta-bility properties and accuracy goals will be discussed. Non-stationary time evolution for their performance tests willbe presented as well.

Tae-Chang JoInha Universitytaechang@inha.ac.kr

Roberto CamassaUniversity of North Carolinacamassa@amath.unc.edu

Generation of Provably Correct CurvilinearMeshes

The development of high-order numerical technologies forCFD is underway for many years now. In many contribu-tions, it is shown that the accuracy of the method stronglydepends of the accuracy of the geometrical discretization.In other words, the following question is raised:we havethe high order methods, but how do we get the meshes?This talk focus on the generation of highly curved oceanmeshes. We propose a robust procedure that allows tobuild a curvilinear mesh for which every element is guar-anteed to be valid. The technique builds on standard opti-mization method (BICG) combined with a log-barrier ob-jective function to guarantee the positivity of the elements

86 GS13 Abstracts

Jacobian. To be valid is not the only requirement for agood-quality mesh. If the temporal discretization is ex-plicit, even a valid element can lead to a very stringentconstraint on the stable time step. The optimization ofthe curvilinear ocean meshes to obtain large stable timesteps is also analyzed.

Jonathan LambrechtsUniversite catholique de Louvainjonathan.lambrechts@uclouvain.be

Jean-Francois Remacle, Thomas ToulorgeUniv. catholique de Louvainjean-franois remacle ¡jean-francois.remacle@uclou,thomas.toulorge@uclouvain.be

Vincent LegatUniversite catholique de LouvainBelgiumvincent.legat@uclouvain.be

Unsteady Nonlinear Gravity Waves in Water of Fi-nite Depth

In this work, we consider two-dimensional gravity wavesgenerated by a moving pressure distribution in water offinite depth. The fully nonlinear model in Euler equa-tion form is solved numerically by the mixed Eulerian andLagrangian approach. The stability of gravity waves forsubcritical and supercritical flows is presented. Subcriti-cal flow solution approaches limiting Stoke’s wave for highamplitude applied pressure while a solitary wave trappedby a localized pressure is detected for supercritical flows.

Montri MaleewongDepartment of Mathematics, Faculty of ScienceKasetsart UniversityMontri.M@ku.ac.th

An Efficient Parallel Implementation of MultirateSchemes for Ocean Modeling

Although explicit time integration schemes require smallcomputational efforts per time step, their efficiency isseverely restricted by stability limits. In particular, un-structured meshes can lead to a very restrictive global sta-ble time step. Multirate methods offer a way to increasethe efficiency by gathering grid cells in appropriate groups.The parallelization of these schemes is challenging becausegrid cells have different workloads. We propose a strategythat shares the workload almost equitably between all pro-cessors at every multirate stage. Performance analyses areprovided for ocean modeling applications.

Bruno Seny, Jonathan LambrechtsUniversite catholique de Louvainbruno.seny@uclouvain.be, jonathan lambrechts¡jonathan.lambrechts@uclouvain

Jean-Francois RemacleUniversite catholique de Louvainjean-francois.remacle@uclouvain.be

An Unstructured Approach to Ocean Wave-Generation Modeling.

Ocean surface gravity waves are an important componentof the atmospheric and oceanic boundary layer and the in-clusion of such in a global climate model has the potentialto correct model biases and improve air-sea interactions.However, existing wave-generation models used for weatherforecasting are computational expensive and ill-suited forstudying polar-ice-free scenarios. Here, a comparison ofan unstructured node approach (using RBF-generated fi-nite differences) will be presented as well as an update onthe the coupled wave-generation component to the NCARCommunity Earth System Model.

Adrean WebbUniversity of Colorado at BoulderCooperative Institute for Research in EnvironmentalSciencesadrean.webb@gmail.com

Synthetic Wavelet Using a Hydrographic Data:Comparing Methods to Solve It

Recently the seismic method is applied in water columnin the ocean, looking for mesoescales features. For thisprocess is necessary to use hydrographic data to fit seis-mic image data. Was compared the traditional methodand the method that Ruddick et al. (2009) suggested, tocalculate the acoustic impedance, reflectivity and wavelet.Though there are lightly differences, results show that thetraditional method is more accuracy for calculation to thesynthetic wavelets than other suggestion.

Ana M. Gonzalez-OrdunoPosgrado de Ciencias del Mar y Limnologia, UNAMglezoa@hotmail.com

Jaime Urrutia FucugauchiInstituto de Geofisica, UNAMjuf@geofisica.unam.mx

Maria Adela Monreal-GomezInstituto de Ciencias del Mar y LimnologiaUNAMmonreal@cmarl.unam.mx

Guillermo Perez-CruzFacultad de Ingenieria, UNAMgapc08@gmail.com

David Alberto Salas-De-LeonInstituto de Ciencias del Mar y LimnologiaUNAMdavid.alberto.salas.de.leon@gmail.com

Using Chaos in Groundwater Remediation

Ineffective mixing constrains groundwater remediation,limiting reactions between contaminants and treatment so-lutions. We address this constraint with chaos, using engi-neered injection and extraction to stretch and fold a plumeof treatment solution. The periodic points of this flow canbe elliptic (poor mixing) or hyperbolic (good mixing); themanifolds of hyperbolic periodic points reveal the asymp-

GS13 Abstracts 87

totic plume geometry; adjusting the magnitude of water in-jected generates a bifurcation structure that provides guid-ance for remediation system optimization.

David C. MaysUniversity of Colorado Denverdavid.mays@ucdenver.edu

Roseanna NeupauerUniversity of Colorado Boulderroseanna.neupauer@colorado.edu

James D. MeissUniversity of ColoradoDept of Applied Mathematicsjdm@colorado.edu

Uncertainty Quantification for Transport Problemsin the Shallow Subsurface

We model heat transport in the shallow subsurface usinga parabolic differential equation together with initial con-ditions and boundary conditions. The parameters in themodel may be related by a mixture model, making theproblem more complex. In this work we use Markov ChainMonte Carlo methods to solve the parameter calibrationproblem.

Anna Meade, Tim KelleyNorth Carolina State Universityanna.meade@gmail.com, tim kelley@ncsu.edu

Owen EslingerUS Army Research and Development Centerowen.j.eslinger@erdc.dren.mil

Optimizing In Situ Groundwater Remediation withEngineered Injection and Extraction

Groundwater remediation requires mixing in aquifers,which can be enhanced using engineered injection and ex-traction (EIE), in which transient flow fields are inducedusing a sequence of injections and extractions of clean wa-ter at wells surrounding the contaminant plume. This pre-sentation uses a multiobjective evolutionary algorithm todetermine a set of EIE sequences that balance multiple ob-jectives, such as maximizing the amount of reaction whileminimizing the treatment solution required and the con-taminant mass extracted.

Amy N. PiscopoUniversity of Colorado Boulderamy.piscopo@colorado.edu

Joseph R. KasprzykDepartment of Civil and Environmental EngineeringThe Pennsylvania State Universityjrk301@psu.edu

Roseanna NeupauerUniversity of Colorado Boulderroseanna.neupauer@colorado.edu

David C. MaysUniversity of Colorado Denverdavid.mays@ucdenver.edu

Homogenization in Case of Transient Motion of aFluid Through a Porous Medium.

We consider transient motion of a fluid through a mediumwith periodic structure of pores. We use a homogeniza-tion procedure to carry out a multiple-scale asymptoticanalysis. The determination of the components of effectivepermeability tensor is reduced to the numerical solution ofperiodic problems in cells. We find that the dependence ofthe viscosity and drag coefficient on the pressure can havea significant effect on the nature of the solution.

Viktoria SavatorovaPhysics Department,National Research Nuclear Universitysvl97@rambler.ru, vsavatorova@gmail.com

Alexander VlasovInstitute of Applied Mechanics Russian Academy ofSciencebah1955@yandex.ru

Alexey TalonovNRNU MEPhItalonov12@rambler.ru

Uncertainty Quantification in Subsurface Flowswith Stochastic Hydrological Laws

The effects of uncertainty in hydrological laws are studiedon subsurface flows modeled by Richards’ equation. One-dimensional infiltration problems are treated and the influ-ence of the variability of the input parameters on the po-sition and the spreading of the wetting front is evaluated.A Polynomial Chaos expansion (with a non-intrusive spec-tral projection) is used. Test cases with different laws arepresented and demonstrate that second order expansionsare well-adapted to represent our quantities of interest.

Pierre SochalaBRGMp.sochala@brgm.fr

Olivier P. Le MaitreLIMSI-CNRSolm@limsi.fr

Shear Banding in a Partially Molten Mantle

We investigate the nonlinear behaviour of partially moltenmantle material under shear. Numerical models of com-paction and advection-diffusion of a porous matrix with aspherical inclusion are built using the automated code gen-eration package FEniCS. The time evolution of melt distri-bution with increasing shear in these models is comparedto laboratory experiments that show high-porosity shearbanding in the medium and pressure shadows around theinclusion.

Laura Alisic, John RudgeBullard LaboratoriesUniversity of Cambridgela339@cam.ac.uk, jfr23@cam.ac.uk

Garth WellsDepartment of Engineering

88 GS13 Abstracts

University of Cambridgegnw20@cam.ac.uk

Richard F. Katz, Sander RhebergenUniversity of OxfordRichard.Katz@earth.ox.ac.uk, sanderr@earth.ox.ac.uk

Fracture Indicators for the Localization of Frac-tures in Porous Medium

We are concerned with the determination of the locationand the permeability of fractures in a porous medium. Weuse a reduced, discrete fracture, flow model for the forwardproblem, and to solve the inverse problem we minimize aleast squares function evaluating the misfit between givenpressure measurements and the calculated pressure. Thesought fractures are obtained iteratively using fracture in-dicators inspired by the idea of refinement indicators. Thefirst numerical results are promising.

Fatma CheikhInria Paris-Rocquencourtcheikhfatmaenit@yahoo.fr

Hend Ben AmeurENIT LAMSINhbenameur@yahoo.ca

Guy ChaventINRIAUniversite Paris-Dauphineguy.chavent@inria.fr

Francois ClementInria Paris-Rocquencourtfrancois.clement@inria.fr

Vincent MartinUTCvincent.martin@utc.fr

Jean E. RobertsINRIA Paris-RocquencourtFrancejean.roberts@inria.fr

Heterogeneous Material Properties and Off-FaultPlastic Response in Earthquake Cycle Simulations

We have developed a numerical method for studying howheterogeneous material properties and off-fault plasticityaffect the earthquake cycle. The fault is governed by anonlinear friction law and we discretize the medium usingsummation-by-parts finite difference operators and weakenforcement of boundary conditions. Our time steppingmethod is capable of handling multiple time scales, effi-ciently integrating the system through both an interseismicperiod and into earthquake rupture.

Brittany A. EricksonStanford Universitybaericks@stanford.edu

Eric M. DunhamDepartment of GeophysicsStanford University

edunham@stanford.edu

Variational Methods for a Problem of Rate- andState-Dependent Friction

Rate- and state-dependent (RS) friction is a standardmodel in geophysics. We consider a problem of RS fric-tion between an elastic body and a rigid foundation, theweak form of which can be written as a coupling of varia-tional equations (VEs). This problem is discretised in time,yielding elliptic VEs. We give some answers to the ques-tion of existence and uniqueness of solutions and present anumerical algorithm based on Finite Elements and a fixedpoint iteration.

Elias PippingFree University of BerlinMathematical Institutepipping@math.fu-berlin.de

Bayesian Selection of Models for the Near Real-Time Earthquake Source Inversion

We present results of quantitative Bayesianranking, underuncertainty, of kinematic earthquakerupture modelswithrespect to their ability to replicate recorded seismic data.This work on rigorously quantifying uncertainties in earth-quake models is part ofour research on Bayesian near real-time earthquake source inversion, withthe long term ob-jective of helping to mitigate human and economical loss-esin case of large earthquakes that possibly may generatetsunamis.

Martin MaiKAUSTmartin.mai@kaust.edu.sa

Ernesto E. PrudencioInstitute for Computational Engineering and SciencesUniversity of Texas at Austinprudenci@ices.utexas.edu

Olaf ZielkeDivision of Earth Science and EngineeringKing Abdullah University of Science and Technologyolaf.zielke@kaust.edu.sa

An Immersed Interface Method for a 1D Poroelas-ticity Problem with Discontinuous Coefficients

We introduce an immersed interface method (IIM) basedon a staggered grid for the 1D poroelasticity equations(Biot model) when the coefficients have discontinuitiesalong material interfaces. The IIM uses standard finite dif-ference method away from the interface and modifies thenumerical schemes near or on the interface to treat the ir-regularities. We will derive and analyze the new method,and show some numerical results to confirm the theoreticalerror estimates.

Son-Young Yi, Maranda BeanThe University of Texas at El Pasosyi@utep.edu, mlbean@miners.utep.edu

GS13 Abstracts 89

High-Order and Low-Cost Stabilized Finite Ele-ment Solvers of Primitive Equations

We present in this talk an anlisis technique for somepenalty stabilized solvers for the Navier-Stokes equations.We consider low-order and high-order methods. The low-order method is a pure penalty method, while the high-order one is a projection-stabilized method. For thismethod the projection operator is generalized to a locallystable interpolation operator. We perform their numericalanalysis (stability and convergence) for unsteady flows. Inthis analysis, the stability is based upon specific inf-supconditions. No local orthogonality properties are neededfor the projection-interpolation operator. The convergenceis based upon the representation of the stabilizing termsby means of bubble finite element spaces. We include somenumerical tests for realistic flows.

Tomas L. Chacon RebolloUniversity of SevillaDepartamento de Ecuaciones Diferenciales y AnalisisNumericochacon@us.es

Large Eddy Simulation of the Quasi-GeostrophicEquations

This talk surveys some recent developments in the mod-eling, analysis and numerical simulation of the quasi-geostrophic equations, which describe the wind-drivenlarge scale ocean circulation. A new large eddy simulationmodel, which is based on approximate deconvolution, isproposed for the numerical simulation of the one-layer andtwo-layer quasi-geostrophic equations. A finite element dis-cretization of the streamfunction formulation of the quasi-geostrophic equations is also proposed. This conformingdiscretization employs the Argyris element. Optimal errorestimates are derived. To the best of our knowledge, theseare the first optimal error estimates for the finite elementdiscretization of the quasi-geostrophic equations. Numeri-cal experiments that support the theoretical estimates arealso presented.

Traian IliescuDepartment of MathematicsVirginia Techiliescu@vt.edu

Assessments of Discretizations of Convection-Dominated Scalar Problems

Oceanic flow models include often convection-dominatedscalar equations that model the transport of species (salin-ity) or temperature. It is well known that stabilized dis-cretizations are necessary for this kind of equations. Thistalk presents a review about our recent experience withstabilized finite element and finite difference methods.

Volker JohnWeierstrass Institute for Applied Analysis and StochasticsResearch Group Numerical Mathematics and Sci.Computingjohn@wias-berlin.de

High Performance Adaptive Finite ElementMethod for Ocean Models

We present a computational framework based on paralleladaptive FEM for ocean simulations. In order to achieveefficient representation of spatial scales we use adaptivemesh refinement based on goal oriented a posteriori errorcontrol. The framework can utilize massively parallel ar-chitecture to achieve the required model resolution. In ourframework we treat the ocean as a turbulent incompress-ible fluid with variable density. We conclude this talk withresults on the ongoing work.

Kaspar MullerSchool of Computer Science and ComunicationRoyal Institute of Technology KTHkasparm@kth.se

Johan HoffmanRoyal Institute of Technology KTHjhoffman@kth.se

Boundary Conditions for the Inviscid Linear andNonlinear Shallow Water Equations in Space Di-mension One and Two

Motivated by problems of geophysical fluid mechanics, wederive a set of boundary conditions which are suitable forthe inviscid Shallow Water equations in space dimensionone and two. For the linearized two-dimensional equa-tions, five different cases occur depending on the back-ground flow.

Roger M. TemamInst. f. Scientific Comput. and Appl. Math.Indiana Universitytemam@indiana.edu

Arthur Bousquet, Aimin HuangIndiana University BloomingtonDepartment of Mathematicsarth.bousquet@gmail.com, aimhuang@indiana.edu

Madalina PetcuUniversite de PoitiersLaboratoire de mathematiques et applicationsmadalina.petcu@math.univ-poitiers.fr

Investigation of Pore-Scale Processes with the Vol-ume of Fluid Method

Recent advances in computational facilities enable to simu-late two-phase flow with sub-pore resolution. These simu-lations can be used to investigate the limits of the clas-sical continuum approach and devise alternative Darcyscale models. We present Navier-Stokes simulations of two-phase flow in complex geometry, using the Volume of Fluidmethod. Particular attention is paid to investigate finger-ing, trapping, corner and film flow and their impact on thecapillary pressure-saturation relationship.

Andrea FerrariInstitute of GeophysicsUniversity of Lausanneandrea.ferrari@unil.ch

90 GS13 Abstracts

Ivan LunatiUniversity of Lausanneivan.lunati@unil.ch

Computation of Three-Phase Fluid Configurationsat the Pore Scale by a Variational Level Set Method

We present a variational level set method to simulatecapillary-controlled displacement of three fluids in 3D porestructures. The evolutionary level set equations for eachfluid is derived based on constrained energy minimizationin the pore space, whereas contact angle formation are en-forced at the zero level sets in the solid. The method is ap-plied to simulate equilibrium fluid configurations and thecorresponding mean and principal interface curvatures insmall subsets of 3D rock images.

Johan HellandSenior Research EngineerInternational Research Institute of Stavangerjohan.olav.helland@iris.no

Espen JettestuenResearch ScientistInternational Research Institute of Stavangereje@iris.no

Kinetic Methods for Pore-Scale Simulations ofCoupled Transport Problems

In our presentation we will present three-dimensional tran-sient pore-scale simulations based on Lattice-Boltzmannmodels for coupled transport problems in porous media in-cluding multiple phases and components, thermal effectsand interaction with electric and magnetic fields. Afteran introduction of the basic kinetic models we will discussthe suitability of our approach both in terms of modelingaccuracy as well as numerical efficiency.

Manfred KrafczykTech. Univ. of BraunschweigGermanykraft@irmb.tu-bs.de

Maik Stiebler, Ying WangInst. for Computational Modeling in Civil EngineeringTU Braunschweigstiebler@irmb.tu-bs.de, wang@irmb.tu-bs.de

Pore-Network Modeling of Reactive Transport un-der (Variably-)Saturated Conditions

A modular pore scale model is developed to study reactiveand adsorptive transport under (variably-) saturated con-ditions, looking at various applications. The continuumporous structure is discretize into a network of pore bod-ies and pore throats, both with finite volumes. For eachpore element, transport of solute is calculated by solvingthe governing mass balance equations, while chemical reac-tion of the fluid phase with reactive solid components maychange the pore geometries.

Amir RaoofUniversity of Utrecht, Netherlandsraoof@geo.uu.nl

S. Majid Hassanizadeh, Chris SpiersUtrecht Universitys.m.hassanizadeh@uu.nl, c.j.spiers@uu.nl

Pore Scale Modeling of Two and Three Phase Flowand Transport Through Porous Media: Where AreWe and What Is to Be Done?

In this talk, I will review one pore scale modeling approachfrom rock reconstruction to network extraction and subse-quent flow modeling using network modelling. Examplesapplying this approach in both two and three phase floware discussed. In particular, the role of wettability of theporous medium on multiphase flow physics will be studied.Future research directions in this area will be consideredand the prospect for true prediction of macroscopic flowparameters is assessed.

Ken SorbieDepartment of Petroleum EngineeringHeriot-Watt Universityken.sorbie@pet.hw.ac.uk

An Efficient Finite Volume Discretization to Sim-ulate Flows on 3D Discrete Fracture Network forTransient Flow Analysis and Equivalent Permeabil-ity Upscaling

The organization of natural fracture networks induces flowpaths that control fluid flows in reservoirs. Taking intoaccount all heterogeneities is computationally very costly,therefore, equivalent multi-porosity and multi-permeabilitymodels have to be used. We present an innovating dis-cretization procedure allowing to simulate flow on 3D Dis-crete Fracture Networks involving over 100.000 fractures.We then demonstrate how to improve the computation ofan equivalent permeability tensor by combining analyticaland clever-meshed numerical solutions.

Matthieu Delorme, Nina Khvoenkova, Benoit NoetingerIFP Energies nouvellesmatthieu.delorme@ifpen.fr, nina.khvoenkova@ifpen.fr,benoit.noetinger@ifpen.fr

Michel QuintardInstitut de Mecanique des Fluides de Toulousequintard@imft.fr

An Interface Fault Model for Sedimentary BasinSimulation

We present an interface fault model which is compatiblewith basin modeling. It considers that the fault zone isrepresented by two interfaces, one for each side of the faultthat is meshed conformal with its neighboring block andthat can move relatively to the other side. Combined witha Finite Volume discretisation, this approach leads to fault-fault fluxes across fault faces that do not match. Resultsfor one-phase and two phase flow are shown.

Isabelle FailleIFP Energies NouvellesFranceisabelle.faille@ifpenergiesnouvelles.fr

GS13 Abstracts 91

Marie Christine Cacas, Sylvain Desroziers, Pascal Have,francoise Willien, Sylvie WolfIFP Energies Nouvellesmarie-christine.cacas@ifpen.fr, sylvain.desroziers@ifpen.fr,pascal.have@ifpen.fr, francoise.willien@ifpen.fr,sylvie.wolf@ifpen.fr

Flow Modeling Techniques for Fractured Reser-voirs - Gridding, Discretization, and Upscaling

Detailed procedures for constructing upscaled fracturemodels are presented. Fine-scale models are formed bycombining sets of triangulated surfaces, and discretiza-tion is accomplished using discrete fracture modeling tech-niques. Coarse cells are formed by agglomerating fine-grid cells, and new flow-based upscaling techniques pro-vide coarse-grid transmissibilities. The local pressure fieldsneeded for upscaling are constructed using linear combi-nations of (pre-computed) large-scale pressure solutions.Simulations of flow through 3D fractured reservoirs demon-strate the accuracy of the proposed techniques.

Mohammad Karimi-FardStanfordkarimi@stanford.edu

Lou J. DurlofskyStanford UniversityDept of Petroleum Engineeringlou@stanford.edu

Is Discrete-Fracture Modeling Helpful for Reser-voir Engineer?

Discrete fracture and matrix modelling and flow simulationof detailed small-scale representation of heterogeneities arenot routinely used for fractured reservoirs studies, evenfor upscaling purposes, to field-scale simulation with dualporosity approach. However new techniques and tools arenow available. Could such DFM models be of any use forthe reservoir engineer? If so, in which situation, and howit impacts our workflow today and in the future? Practicalexamples will illustrate our works in this domain.

Alexandre LapeneEnergy Resources Engineering, Stanford.alexandre.lapene@total.com

Olivier GosselinTOTAL E&P FranceImperial Collegeolivier.gosseling@total.com

Luc PaugetTOTAL E&P Franceluc.pauget@total.com

Discretizing Fractured Porous Media for Multi-phase Flow Simulation

Adaptive discretization is key for physically realistic andefficient simulation of multiphase fluid flow through porousrock with discrete fractures. For goal-based simulation,where space-time accuracy is predefined by the user, spatialdiscretization errors need to be dealt with using an error

metric. In the discretization of time, stepping needs toadapt to the wide range of flow velocities. Here we presentmodels of fractured rock where discretization is adapted tofracture geometry, fluid-pressure-error and flow speed.

Stephan K. MatthaiMontan University of LeobenLeoben, Austriastephan.matthai@gmail.com

Multiphase Flow, Deformation and Wave Propaga-tion in Porous Media

Single and multiphase flows are determined by LatticeBoltzmann Models and elastic deformations of the solidmatrix by Lattice Spring Models. These two codes arecoupled by using a momentum exchange. Then, wavepropagation is addressed either by direct simulations orhomogeneization. A few comparisons with analytical so-lutions or results obtained by different numerical methodsare given. Some applications to real porous media, possi-bilities and extensions of these codes are discussed.

Pierre AdlerUniversite Pierre et Marie CurieFrancepierre.adler@upmc.fr

Aliaksei PazdniakouSisypheUniversite Pierre et Marie Curiealiaksei.pazdniakou@upmc.fr

Mixed Mortar Methods for Flow in HeterogeneousPorous Media

With the equation in mixed form, we use a nonoverlap-ping mortar domain decomposition method, which is effi-cient in parallel if the mortar space is small. We defineformally first and second order multiscale mortar spacesusing homogenization. For locally periodic permeability,the method achieves optimal order error estimates in themesh spacing and heterogeneity period. Otherwise, numer-ical results show the method works well. It can be adaptedas a two-level solver for the fine-scale system.

Zhen TaoInstitute for Computational Engineering and SciencesThe University of Texas at Austintaozhen@ices.utexas.edu

Hailong XiaoICESThe University of Texas at Austinxiaohl@ices.utexas.edu

Theoretical and Computational Perspectives onChemical Enhanced Oil Recovery Processes

In this talk, I will give a brief overview of some of the fun-

92 GS13 Abstracts

damental theoretical and computational problems in EORtechnology that are of interest to the speaker. Then I willgive some recent results on some of these problems ob-tained by the speaker and his collaborators. The researchto be presented has been made possible by a grant (NPRP08-777-1-141) from the Qatar National Research Fund (amember of The Qatar Foundation).

Prabir DaripaTexas A&M UniversityDepartment of Mathematicsprabir.daripa@math.tamu.edu

The Riemann Problem for Three-Phase Flow

We focus on a particular system of two conservation lawswhich models immiscible flow in porous media relevant forpetroleum engineering. The Riemann solutions are foundfor a range of initial conditions important in applications,representing the injection of two fluids (water, gas) into ahorizontal reservoir containing a third fluid (oil) to be dis-placed. Despite loss of strict hyperbolicity, the solutionsfor each data exists and is unique. Also, it depends L1

continuously on the Riemann data. Such solutions alwaysdisplay a lead shock involving one of the injected fluids andthe fluid already present. There is a threshold solution sep-arating solutions according to which of the injected fluidsis present in the lead shock.

Frederico C. FurtadoUniversity of WyomingDept of Mathematicsfurtado@uwyo.edu

Arthur AzevedoUniversity of Brasiliaarthurvazevedo@gmail.com

Aparecido de SouzaFederal University of Campina Grandecidodesouza@gmail.com

Dan MarchesinInstituto Nacional de Matematica Pura e Aplicadamarchesi@impa.br

Modelling and Computation of ThermohalineGroundwater Flows

We study salinity- and thermohaline-flow in fracturedporous media. We adopt two approaches: (i) the frac-tures are treated as thin flow subregions having the samedimension as medium in which they are embedded; (ii) thefractures are regarded as manifolds of reduced dimension.We discuss the validity of both approaches and, in the caseof salinity-driven flow, investigate the deviations of the re-sults determined by employing the Forchheimer correctionwith those predicted by Darcy’s law.

Alfio GrilloDept. of Mathematical SciencesPolythecnic of Turin, Italyalfio.grillo@polito.it

Dmitry Logashenko, Sabine StichelGoethe Center for Scientific ComputingGoethe University Frankfurt a.M.

dimitriy.logashenko@gcsc.uni-frankfurt.de,sabine.stichel@gcsc.uni-frankfurt.de

Gabriel WittumGoethe Center for Scientific ComputingGoethe University Frankfurtwittum@gcsc.uni-frankfurt.de

A Unified Fe Approach for Wave Propagation inElastic Media - from Near Incompressibility toAcoustics

The CMU Quake group has been working on large-scaleearthquake simulations using Hercules –an octree-basedfinite-element wave propagation simulator. This code isbased on trilinear displacement elements. One limitationis its inability to provide reliable results for low S- to P-wave velocity ratios. Here, we assess the performance of aquadratic displacement-based formulation versus that of amixed displacement-pressure formulation for nearly incom-pressible and acoustic wave-propagation applications, andexplore their applicability to gravity waves.

Jacobo BielakCarnegie Mellon UniversityDepartment of Civil & Env. Engbielak@cs.cmu.edu

Haydar KaraogluCarnegie Mellon Universityhkaraogl@cmu.edu

High Order One-Step Pnpm Schemes on Unstruc-tured Meshes for Hyperbolic Balance Laws

In this talk we present a new unified approach of generalPNPM schemes on unstructured meshes in two and threespace dimensions for the solution of time–dependent partialdifferential equations, in particular hyperbolic conservationlaws. The new PNPM approach uses piecewise polynomi-als uh of degree N to represent the data in each cell. Forthe computation of fluxes and source terms, another set ofpiecewise polynomials wh of degree M ≥ N is used, whichis computed from the underlying polynomials uh using areconstruction or recovery operator. The PNPM methodcontains classical high order finite volume schemes (N = 0)and high order discontinuous Galerkin (DG) finite elementmethods (N = M) just as two particular special cases of amore general class of numerical schemes. Our method alsouses a novel high order accurate one–step time discretiza-tion, based on a local space–time discontinuous Galerkinpredictor, which is also able to solve PDE with stiff sourceterms.

Michael DumbserUniversität StuttgartGermanymichael.dumbser@ing.unitn.it

Large-Scale Bayesian Seismic Inversion

We present a computational framework for solution ofdiscretized infinite-dimensional Bayesian inverse problems.We address several computational issues related to theappropriate choice of prior, consistent discretizations,

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tractable treatment of the Hessian of log posterior, andscalable parallel MCMC algorithms for sampling the pos-terior. We apply the framework to the problem of globalseismic inversion, for which we demonstrate scalability to1M earth parameters, 630M wave propagation unknowns,and 100K cores on the Jaguar supercomputer.

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

Carsten BursteddeInstitut fuer Numerische SimulationUniversitaet Bonnburstedde@ins.uni-bonn.de

Tan Bui-ThanhThe University of Texas at Austintanbui@ices.utexas.edu

James R. MartinUniversity of Texas at AustinInstitute for Computational Engineering and Sciencesjmartin@ices.utexas.edu

Georg StadlerUniversity of Texas at Austingeorgst@ices.utexas.edu

Lucas WilcoxDepartment of Applied MathematicsNaval Postgraduate Schoollwilcox@nps.edu

High-Order Explicit Local Time-Stepping Methodsfor Wave Propagation

We propose high-order explicit local time-stepping (LTS)schemes based either on classical or low-storage Runge-Kutta schemes for the simulation of wave phenomena. Byusing smaller time steps precisely where smaller elementsin the mesh are located, these methods overcome the bot-tleneck caused by local mesh refinement in explicit timeintegrators. In (J. Diaz and M.J. Grote, Energy conserv-ing explicit local time-stepping for second-order wave equa-tions, SIAM J. Sci. Comput., 31 (2009), pp. 1985–2014.),explicit second-order LTS integrators for transient wavemotion were developed, which are based on the standardleap-frog scheme. In the absence of damping, these time-stepping schemes, when combined with the modified equa-tion approach, yield methods of arbitrarily high (even) or-der. To achieve arbitrarily high accuracy in the presenceof damping, while remaining fully explicit, explicit LTSmethods for the scalar damped wave equation based onAdams-Bashforth multi-step schemes were derived in (M.J. Grote and T. Mitkova, High-order explicit local time-stepping methods for damped wave equations, J. Comput.Appl. Math., 239 (2013), pp. 270–289). Here we proposeexplicit LTS methods of high accuracy based either on ex-plicit classical or low-storage Runge-Kutta (RK) schemes.In contrast to Adams-Bashforth methods, RK methods areone-step methods; hence, they do not require a startingprocedure and easily accommodate adaptive time-step se-lection. Although RK methods do require several furtherevaluations per time-step, that additional work is compen-sated by a less stringent CFL stability condition.

Marcus J. Grote

Universitat Baselmarcus.grote@unibas.ch

Michaela MehlinUniversity of Baselmichaela.mehlin@unibas.ch

Teodora MitkovaUniversity of Fribourgteodora.mitkova@unifr.ch

High-Performance 3D Numerical Simulations forSeismic Scenarios: An Engineering Perspective

In spite of the progress in computational tools for seismicwave propagation, the vast majority of engineering studiesare still routinely performed using 1D approaches, relyingon the assumption of vertical plane wave propagation in ahorizontally layered soil. Although this is a rational ap-proach for many engineering applications, it may provideunrealistic results when applied to earthquake ground mo-tion prediction and to the generation of ground shakingmaps in the vicinity of a seismic fault. Relying on a non-conforming strategy, the SPEED high performance com-puting code (SPectral elements in elastodynamics with Dis-continous Galerkin) has been developed to study complex3D models and provide the capability to simulate seismicwave propagation from the source to the structure. Thismay open new perspectives to solve earthquake engineeringproblems.

Roberto PaolucciDepartment of Structural EngineeringPolitecnico di Milanopaolucci@stru.polimi.it

Paola F. Antonietti, Ilario MazzieriPolitecnico di Milanopaola.antonietti@polimi.it, ilario.mazzieri@mail.polimi.it

Roberto Guidotti, Chiara SmerziniDipartimento di Ingegneria StrutturalePolitecnico di Milanoguidotti@stru.polimi.it, csmerzini@stru.polimi.it

Marco StupazziniMunich REmstupazzini@munichre.com

Hybrid Multiscale Finite-Volume Galerkin Methodfor Elliptic and Parabolic Problems

The iterative multiscale finite-volume method can be re-garded as a domain decomposition method with the partic-ular advantage that conservative fluxes are obtained at anyiteration level. This is of great advantage e.g. for transportin heterogeneous porous media. Recently, enriched multi-scale methods have been proposed to improve robustnessand along this line, here a hybrid multiscale finite-volumeGalerkin (MSFVG) method is introduced.

94 GS13 Abstracts

Davide CortinovisETHcortinovis@ifd.mavt.ethz.ch

Generalized Multiscale Finite Element Methods.

In this talk, we present a general approach called Gener-alized Multiscale Finite Element Method (GMsFEM) forperforming multiscale simulations for problems withoutscale separation over a complex input space. In the pro-posed approach, we present a general procedure to con-struct the offline space that is used for a systematic en-richment of the coarse solution space in the online stage.In the online stage, for any input parameter, a multiscalespace is constructed to solve the global problem on a coarsegrid. We present various examples in the paper and somenumerical results to demonstrate the effectiveness of ourmethod.

Yalchin EfendievDept of MathematicsTexas A&M Universityefendiev@math.tamu.edu

Juan GalvisUniversidad Nacional de Colombiajugal4621@gmail.com

Tom HouClatechhou@cms.caltech.edu

Dynamic Upscaling/downscaling for Multi-PhaseFlow in a Multiscale Finite Volume Framework

We propose an upscaling/downscaling method that isbased on dynamic simulation of a model in which the accu-racy of the upscaled model is continuously monitored viaindirect error-measures. If the error measure is bigger thana specified tolerance, the upscaled model is updated withapproximate fine scale information that is reconstructedfrom a multiscale finite volume method. We apply adaptiveprolongation and restriction operators for flow and trans-port equations in constructing an approximate fine scalesolution.

Seong H. LeeChevron ETCSEON@chevron.com

X WangStanford Universityxcwang@stanford.edu

Rouven KunzeUNILrouven.kunze@unil.ch

Convergent Non-Linear Upscaling for MultiphaseFlow and Transport in Porous Media

Upscaling of nonlinear multiphase flow and transport prob-lems in porous media is challenging, but often necessary tolower computational cost. We propose a method that auto-matically upscales in the appropriate limiting flow regimesand acts as a preconditioner to the fine scale nonlinearsystem otherwise. Communication between the numericalscales is handled by physically based compression and re-construction operators. Further, fine scale computationsare automatically localized to the more demanding regionsof the domain.

Jan Skogestad, Eirik KeilegavlenUniversity of Bergenjan.skogestad@math.uib.no, Eirik.Keilegavlen@uib.no

Multiscale Mortar Methods for Multiphysics Ap-plications

We discuss a multiscale framework for multiphysics prob-lems based on mortar domain decomposition methods. Thedomain is decomposed into a series of subdomains (coarsegrid) with different physical processes, mathematical mod-els, and numerical methods. The equations are discretizedlocally on a fine scale, while interface conditions are im-posed weakly on a coarse scale using mortar finite elements.By eliminating the subdomain unknowns, the global prob-lem is reduced to a coarse scale interface problem that issolved efficiently using a multiscale flux basis. Applicationsto Stokes - Darcy and porous media flow - geomechanicscouplings are presented.

Ivan YotovUniveristy of PittsburghDepartment of Mathematicsyotov@math.pitt.edu

Applications of Shaping Regularization in Geo-physical Inverse Problems

Shaping regularization is a general framework for solvinginverse problems. Instead of specifying an objective func-tion for optimization, shaping requires a forward operator,a backward (approximate inverse) operator, and a modelshaping operator, which can be a projection of the esti-mated model into the space of acceptable models. I willshow several examples of using shaping regularization ingeophysical inverse problems: data regularization, simulta-neous source separation, and seismic velocity estimation.

Sergey FomelUniversity of Texas at Austinsergey.fomel@beg.utexas.edu

GS13 Abstracts 95

Inversion of Large Scale Electromagnetic Data

Abstract not available at time of publication.

Eldad HaberDepartment of MathematicsThe University of British Columbiahaber@math.ubc.ca

Full Waveform Inversion of Blended Data: Analysisof Multi-frequency Inversion Strategies

One way to reduce the overall cost of waveform inversionis via the adoption of blended or simultaneous sources,where multiple sources are simultaneously fired with ran-dom time delays. This can be achieved by assemblingmultiple sources into super-shots. In the present study,we examine the effect of different multi-frequency selectionstrategies on the inversion of complex velocity models withdata that simulate a simultaneous source acquisition.

Mauricio D. Sacchi, Amsalu Y. AnagawUniversity of Albertamsacchi@ualberta.ca, aanagaw@ualberta.ca

Coupling Two-Phase CompositionalPorous-Medium and Free Flow

The numerical simulation of flow and transport phenom-ena in porous media is quite often based on Darcy’s law,whereas in free flow regions the Navier-Stokes model hasto be used. Of special interest are structures composed ofa porous part and an adjacent free flowing fluid. So far,the coupling of free flow with porous medium flow has beenconsidered only for a single-phase system. We extend thisclassical concept to two-component non-isothermal flowwith two phases inside the porous medium and a singlephase inside the free flow region. Our coupling concept alsotakes into account evaporation and condensation processesat the interface. We discuss our new model and introducedifferent coupling conditions. Moreover, some numericalexamples illustrate the coupling between the two modeldomains.

Rainer HelmigIWS, University of Stuttgart, GermanyInstitut fur Wasserbaurainer.helmig@iws.uni-stuttgart.de

Klaus MosthafUniversitaet Stuttgart, IWSklaus.mosthaf@iws.uni-stuttgart.de

Katherina BaberDept. of HydromechanicsUniversity of Stuttgartkatherina.baber@iws.uni-stuttgart.de

Bernd FlemischUniversity of Stuttgart, Germanybernd.flemisch@iws.uni-stuttgart.de

Space-Time Domain Decomposition for Porous

Media Flow and Transport

We present two non-overlapping domain decomposi-tion methods for solving heterogeneous time-dependentadvection-diffusion problems in a mixed formulation:a time-dependent Steklov-Poincare operator with aNeumann-Neumann preconditioner and a Schwarz wave-form relaxation method with optimized transmission con-ditions. Thus, different time steps can be used in differentsubdomains adapted to their physical properties. We de-rive the formulations using a splitting approach. We shownumerical results in 2D on a simplified test case suggestedby the nuclear waste disposal problems.

Thi-Thao-Phuong HoangINRIA Paris-Rocquencourtphuong.hoang thi thao@inria.fr

Jerome JaffreINRIA-Roquencourt78153 Le Chesnay cedex FranceJerome.Jaffre@inria.fr

Caroline JaphetParis 13 university, Francejaphet@math.univ-paris13.fr

”Heterogeneous Domain Decomposition Methodsfor Surface and Saturated/unsaturated GroundWater Flow”

Our approach to the mathematical modelling of coupledsurface and ground water flow is based on Richards equa-tion and a clogging-type coupling to the shallow waterequations or simple compartement models for surface wa-ter. The seepage along river beds and lakes is describedby Signorini-type boundary conditions. We will presentPoincare-Steklov formulations of this heterogeneous prob-lem and an iterative solver of Robin-Neumann-type tak-ing the multiple time scales of ground and surface waterflow into account. We present numerical experiments withmodel problems illustrating the basic properties of our ap-proach, such as mass conservation, as well as the perfor-mance of our iterative scheme.

Ralf KornhuberFU BerlinFachbereich Mathematik und Informatikkornhuber@math.fu-berlin.de

Multidimensional Coupling for Shallow WaterFlows

The motion of water in a complex hydrodynamic config-uration is characterized by a wide spectrum of space andtime scales. Consequently, the numerical simulation of ahydrodynamic system of this type is characterized by alarge computational cost. In the last years a lot of work

96 GS13 Abstracts

has been done concerning 1D-2D coupling. In this talk3D-1D and 3D-2D coupling strategies will be introduced.

Edie Miglio

Politecnico di Milano (Italy)MOX, Dept. of Mathematicsedie.miglio@polimi.it

A Multiscale Formulation Based on CVD-MPFASchemes on Structured and Unstructured Grids

Families of Darcy-flux approximations have been developedfor consistent approximation of the general tensor pres-sure equation arising from Darcy’s law together with massconservation. The schemes are control-volume distributed(CVD) with flow variables and rock properties sharing thesame location in a given control-volume and are comprisedof a multipoint flux family formulation (CVD-MPFA). Theschemes are used to develop a CVD-MPFA based multi-scale formulation applicable to both structured and un-structured grids in two-dimensions.

Michael G. EdwardsSwansea UniversitySchool of Engineeringm.g.edwards@swansea.ac.uk

Elliot ParramoreSwansea Universitye.t.parramore@swansea.ac.uk

Mimetic Finite Difference Methods and Virtual El-ement Discretizations for Porous Media Applica-tions

We present the family of mimetic finite difference meth-ods and of virtual element discretizations and discuss howthese approaches can be used to design efficient schemesto approximate flow and transport models in porous me-dia. The permeability tensor in the diffusive terms may beheterogeneous, full and anisotropic. These numerical tech-niques can be applied to computational meshes of polygo-nal or polyhedral cells with very general shape, also non-conforming as the ones of the Adaptive Mesh Refinement(AMR) method and non-convex, and used to approximatelinear and non-linear models like the Richards equation.

Gianmarco ManziniLos Alamos National Laboratorygm.manzini@gmail.com

Nonlinear Monotone Finite Volume Method forRichards Equation

The Richards equation is often used to model subsurfaceflow in unsaturated media. We present a new nonlinearfinite volume method which guarantees the discrete maxi-mum principle in every subdomain with homogeneous per-meability. In state-of-the-art methods the monotonicity isachieved by using the first order upwind of the relativepermeability which decreases the accuracy of a method.Our approach provides the second order of accuracy forthe pressure which is confirmed by numerical tests.

Daniil Svyatskiy

Los Alamos National Laboratorydasvyat@lanl.gov

Coupling of Stokes and Darcy Flows using Dis-continuous Galerkin and Mimetic Finite DifferenceMethod

We present a numerical method for coupling Stokes andDarcy flows based on discontinuous Galerkin (DG) el-ements for Stokes and mimetic finite difference (MFD)methods for Darcy. Both methods are locally mass conser-vative and can handle irregular grids. The MFD methodsare especially suited for flow in heterogeneous porous me-dia, as they provide accurate approximation for both pres-sure and velocity and can handle discontinuous coefficientsas well as degenerate and non-convex polygonal elements.We develop DG polygonal elements for Stokes, allowing forcoupled discretizations on polygonal grids. Optimal con-vergence is obtained for the coupled numerical method andconfirmed computationally.

Konstantin LipnikovLos Alamos National Laboratorylipnikov@lanl.gov

Danail VassilevUniversity of Exeterd.vassilev@exeter.ac.uk

Nonlinear Discretizations for Multi-Phase Flows inPorous Media

We consider approaches to the design of a monotonecell-centered finite volume discretization of convection-diffusion equations describing multiphase flows. The per-meability tensor may be heterogeneous, full and essen-tially anisotropic. The conformal computational mesh isassumed to consist of convex polygonal or polyhedral cells.The schemes possess the minimal stencil containing theclosest neighboring cells only. The cornerstone of the ap-proaches is the nonlinear discretization of fluxes derivedon faces of mesh cells, see Rus. J. Numer. Anal. Math.Modelling 27(4) 2012 and references therein.

Yuri Vassilevski, Kirill NikitinInstitute of Numerical MathematicsRussian Academy of Sciencesyuri.vassilevski@gmail.com, nikitin.kira@gmail.com

Kirill TerekhovINM RASkirill.terekhov@gmail.com

Equal-order Finite Elements for Hydrostatic FlowEquations of the Ocean

Simulation of flow phenomena in the ocean and in otherlarge but relatively flat basins are typically based onthe primitive equations, which result from application ofthe hydrostatic approximation. We analyze such ”2.5-

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dimensional” systems and formulate stabilized finite ele-ment schemes with equal-order interpolation. We show sta-bility and give an a priori error estimate for several estab-lished stabilized equal-order schemes, as pressure-stabilizedPetrov-Galerkin (PSPG), Galerkin least squares (GLS) andlocal projection schemes (LPS) which are extended here tothe hydrostatic approximation.

Malte BraackChristian-Albrechts-Universitat zu Kielbraack@math.uni-kiel.de

Madlen KimmritzCAU Kielkimmritz@math.uni-kiel.de

Recent Results on Inviscid Limits for the Stochas-tic Navier-Stokes Equations and Related Systems

One of the original motivations for the development ofstochastic partial differential equations traces it’s originsto the study of turbulence. In particular, invariant mea-sures provide a canonical mathematical object connectingthe basic equations of fluid dynamics to the statistical prop-erties of turbulent flows. In this talk we discuss some recentresults concerning inviscid limits in this class of measuresfor the stochastic Navier-Stokes equations and other re-lated systems arising in geophysical and numerical settings.

Nathan Glatt-HoltzIndiana Universitynegh@indiana.edu

Velocity-Pressure Proper Orthogonal Decomposi-tion Methods For Flow Problems

Proper Orthogonal Decomposition is one of the most suc-cessful tools in the context of reduced-order modeling forflow problems modeled by incompressible Navier-Stokesequations. The standard approach in combination withvery common assumptions leads to a reduced-order model(ROM) only for velocity. However, the need for compu-tation of pressure is a given. In this talk, the numericalstudies of some already existing pressure ROMs and of anew one will be presented.

Swetlana SchyschlowaWeierstrass Institute for Applied Analysis and Stochasticsswetlana.schyschlowa@wias-berlin.de

An Ergodic Theory and Harmonic Analysis BasedMethod for Analyzing Ocean Flows

We consider an approach, called the ergodicity defect, foranalyzing ocean flows. The ergodicity defect distinguishesindividual trajectories via their complexity, which in turnallows for the identification of Lagrangian coherent struc-tures. The approach combines the mathematical areasof ergodic theory and harmonic analysis/wavelet theory.The advantages, practical uses, and disadvantages of themethod are discussed and several examples are presented.

Sherry ScottMarquette University

sherry.scott@marquette.edu

Irina Rypina, Lawrence PrattWoods Hole Oceanographic Institutionirypina@whoi.edu, lpratt@whoi.edu

Mike BrownRSMASMiami Universitymbrown@rsmas.miami.edu

Energy Stable Scheme for Shallow Water Equations

The subject of the talk is the numerical solution of shallowwater equations with bathymetry. It is known that in somecases spurious oscillations in the numerical solution mayarise. This is due to the conservation properties of theadopted numerical scheme. In this talks we are going torevise energy stable and energy preserving finite volumescheme in order to end up with an oscillation free method.Some preliminary numerical results are also presented.

Mustafa AltinakarNCCHE - University of Mississippialtinakar@ncche.olemiss.edu

Edie MiglioPolitecnico di Milano (Italy)MOX, Dept. of Mathematicsedie.miglio@polimi.it

Jaswant SinghNCCHE - University of Mississippisingh@ncche.olemiss.edu

Modelling Solute Transport in Meandering Chan-nels using a High-order DG Method

A third-order accurate numerical method for the 2D shal-low water equations, inclusive of the convection-diffusionterms due to the streamlines curvature, is discussed. Thehydrodynamics and the behaviour of a passive contaminantare analyzed, using recent advances in river mechanics andnovel findings in RKDG methods. The comparison withselected laboratory data shows that good results can beobtained using relatively coarse grids, supporting the useof high-order methods in engineering practice.

Valerio Caleffi, Alessandro ValianiUniversity of Ferraravalerio.caleffi@unife.it, alessandro.valiani@unife.it

Comparison Between Sph and Level Set Methodsfor Free Boundary Problems for IncompressibleEuler and Navier-Stokes Equations

A new finite difference ghost cell level set multigrid methodfor the numerical solution of free boundary problems forincompressible Euler and Navier-Stokes equations is pre-sented. The equations are discretized in primitive variableon a fixed Cartesian grid. The free surface is taken intoaccount by a level set function, which is evolved by thenormal velocity of the fluid at the surface. The Poissonequation on the pressure, obtained by the incompressibilitycondition, is efficiently solved by multigrid. Applications

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to some test problems will be presented. The numerical so-lutions will be compared to those obtained by a smoothedparticle hydrodynamic code, in which the incompressibilityis replaced by a weakly compressible equation of state, witha sound speed one order of magnitude larger than a typi-cal flow velocity. The comparison shows a good agreement,and emphasizes the relative merits of the two approaches.

Giovanni RussoUniversity of CataniaDepartment of Mathematicsrusso@dmi.unict.it

Armando CocoDipartimento di Geologia e Geofisica, UNIBAcoco@dmi.unict.it

Giuseppe BilottaDMI, UNICTbilotta@dmi.unict.it

Second-Order Finite Volume Schemes for Geophys-ical Shallow Water Flows with Dynamic Wet-DryFront

We propose a revisiting of second-order finite volumeschemes for 2d shallow water equations. Schemes are basedon a HLLC-type solver according to [Vila86], MUSCL re-constructions and IMEX time schemes, [PaRu05]. Thewell-balanced property is obtained applying the methodof [AuBr05]. We show the efficiency of the direct solver onreal type river flows. Numerical experiments enhance dif-ferences between first and second-order schemes both forlow-water flows and wet-fry front dynamics.

Frederic CoudercCNRS & IMTfrederic.couderc@insa-toulouse.fr

Jerome Monnier, Jean-Paul VilaMathematics Institute of Toulousejerome.monnier@insa-toulouse.fr, vila@insa-toulouse.fr

Geostatistical Inversion under Transient Flow Con-ditions

Geostatistical inversion is a valuable tool for the assess-ment of aquifer permeability. In previous implementationsthe assumption of a stationary flow field and the solution ofone adjoint problem per measurement were necessary. Wepresent an extension of geostatistical inversion methods toinstationary flow regimes. This facilitates the treatmentof variable boundary conditions (e.g. nearby rivers) andlarge data sets. Implementation in the software frameworkDUNE makes high-performance-computing and full paral-lelization available.

Ole KleinInterdisciplinary Center for Scientific ComputingHeidelberg Universityole.klein@iwr.uni-heidelberg.de

Olaf A. CirpkaCenter for Applied GeoscienceUniversity of Tuebingenolaf.cirpka@uni-tuebingen.de

Olaf IppischInterdisziplinary Center for Scientific ComputingUniversity of Heidelbergolaf.ippisch@iwr.uni-heidelberg.de

A Discontinuous Galerkin Based Quasi-Linear Geo-statistical Approach

The quasi-linear geostatistical approach can be used to es-timate the spatial distribution of heterogeneous hydraulicconductivity fields based on point-wise measurements ofobservable quantities. The accurate and efficient solutionof steady-state solute transport problems is crucial for theinversion. The discontinuous Galerkin method incorpo-rates upwinding in a natural way, yielding a robust solvereven in the convection dominated case. The benefits anddrawbacks as compared to the streamline diffusion methodare discussed.

Adrian NgoUniversity of Heidelbergadrian.ngo@iwr.uni-heidelberg.de

Ronnie L. SchwedeCenter for Applied GeoscienceUniversity of Tubingenronnie.schwede@uni-tuebingen.de

Olaf A. CirpkaCenter for Applied GeoscienceUniversity of Tuebingenolaf.cirpka@uni-tuebingen.de

Parameter Estimation by Ensemble Kalman Filterswith Transformed Data: Approach and Applicationto Hydraulic Tomography

EnKFs have been converted to tools for parameter estima-tion in groundwater applications. EnKFs provide optimalparameter estimates only if all involved variables are multi-variate Gaussian. To improve EnKFs, we apply nonlinear,monotonic transformations to the observed states, render-ing them univariate Gaussian. The transform resemblesan implicit quasi-linearization. For illustration of the im-proved convergence, we present a first-time application ofan EnKF to parameter estimation from 3-D hydraulic to-mography in multi-Gaussian log conductivity fields.

Wolfgang Nowaktitute for Modelling Hydraulic and EnvironmentalSystemsUniversity of Stuttgartwolfgang.nowak@iws.uni-stuttgart.de

Anneli SchonigerApplied Geosciences

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University of Tubingenanneli.schoeniger@uni-tuebingen.de

Harrie Jan Hendricks FranssenAgrosphere (IBG-3)Forschungszentrum Julichh.hendricks-franssen@fz-juelich.de

Active and Passive Hydrogeophyscial TomographicSurveys

This talk discusses uniqueness, scale, resolution, and un-certainty issues associated with modeling of flow throughgeologic media. We advocate that stochastic interpreta-tion of non-redundant hydrological data from active andpassive tomographic surveys is the key to the future hy-drological characterization. In conjunction with geophysi-cal monitoring of responses of the subsurface, hydrologicaltomographic surveys/stochastic joint interpretation couldbe the ultimate subsurface characterization methodology.

Tian-Chyi J. YehThe University of Arizonayeh@hwr.arizona.edu

Non-Equilibrium Capillarity Effect at DifferentScales

Various studies have shown that capillary pressure is notonly a function of saturation but also depends on its timerate of change. This is known as the dynamic capillarityeffect. We present an overview of computational and ex-perimental studies on dynamic coefficient and show thatits value increases with the size of domain of interest. Weprovide an explanation for this correlation and discuss con-sequences of scale-dependence of dynamic coefficient forlarge-scale field situations.

Majid HassanizadehUniversity of Utrechthassanizadeh@geo.uu.nl

Simona BotteroDelft University of TechnologyFaculty of Civil Engineering and Geosciencess.bottero@tudelft.nl

Phase Transitions Across Scales: Discrete and Con-tinuum Models

It is known that phase transitions occur differently in bulkfluid than in confined porespace, and constitutive relation-ships at porescale differ from those at macroscale. Atporescale there are discrete and continuum models, and atmacroscale there are continuum models. However, thereare no methods of formal upscaling for nonsmooth non-linear processes representing phase transitions across thesescales. We discuss computational models that bridge thescales for phase transitions in methane hydrate, coalbedmethane, and ground freezing modeling.

Heterogeneous Multiscale Methods for Two-PhaseFlow with Rate-Dependent Extension

Christian RohdeUniversity of StuttgartDepartment of Mathematicscrohde@mathematik.uni-stuttgart.de

Instability Effects in Hysteresis Models for PorousMedia Flow

We present various flow models for unsaturated porous me-dia. Our main interest is the gravity driven penetration ofa dry material, a situation in which fingering effects canbe observed experimentally and numerically. The flow isdescribed by either a Richards or a two-phase model. Theimportant modelling aspect regards the capillary pressurerelation which can include static hysteresis and dynamiccorrections. We report on analytical existence and insta-bility results for the corresponding models and present nu-merical calculations. We show that fingering effects can beobserved in various models and discuss the importance ofthe static hysteresis term.

Ben SchweizerTU DortmundFakultat fur Mathematikben.schweizer@tu-dortmund.de

Convection Driven by Internal Heating

Two-dimensional direct numerical simulations are con-ducted for convection sustained by uniform internal heat-ing in a horizontal fluid layer. Top and bottom bound-ary temperatures are fixed and equal. Prandtl numbersrange from 0.01 to 100, and Rayleigh numbers (R) are upto 5 · 105 times the critical R at the onset of convection.The asymmetry between upward and downward heat fluxesis a quantity without analog in classical Rayleigh-Benardconvection and is found to be non-monotonic in R. Scal-ing arguments previously applied to the Rayleigh-BenardNusselt number are applied to the mean temperature.

David GoluskinMathematics DepartmentColumbia Universitygoluskin@gmail.com

Edward SpiegelDepartment of AstronomyColumbia Universityeas5@columbia.edu

Effects of Velocity and Temperature BoundaryConditions in Turbulent Thermal Convection

We report on results of high resolution direct numeri-cal simulations of two-dimensional Rayleigh-Benard con-vection for Rayleigh numbers up to Ra = 1010 in orderto study the influence of both temperature and velocityboundary conditions on turbulent heat transport. In thefirst scenario, while imposing the no-slip velocity bound-

100 GS13 Abstracts

ary condition, we consider the extreme cases of fixed heatflux and fixed temperature Both cases display identicalheat transport at high Rayleigh numbers fitting a powerlaw Nu ≈ 0.138 × Ra.285 above Ra = 107. The find-ings are compared and contrasted with results of recentthree-dimensional simulations and experiments. In thesecond scenario we consider the setup originally consid-ered by Rayleigh for calculating conditions for the onset ofthermal convection, fixed temperature boundary conditionwith free-slip velocity boundary conditions. Surprisingly,at high Rayleigh numbers a strong shear flow develops withperiodic ’bursting’ of the thermal boundary layers. We’lldiscuss this phenomena and its impact on the heat trans-port.

Hans JohnstonDepartment of Mathematics & StatisticsUniversity of Massachusetts Amherstjohnston@math.umass.edu

David GoluskinMathematics DepartmentColumbia Universitygoluskin@gmail.com

Da ZhuDepartment of Earth, Atmospheric and Planetary ScienceMITdazhu@mit.edu

Glenn FlierlDepartment of Earth, Atmospheric and Planetary ScienceMassachusetts Institute of Technologyglenn@lake.mit.edu

Charles R. DoeringUniversity of MichiganMathematics, Physics and Complex Systemsdoering@umich.edu

Large Scale Patterns in Convection: fromRayleigh-Benard, through Prandtl problem, tomoist atmospheric convection

Large scale patterns formation in dry and moist convectionscenarios are addressed in this paper. The first part of thetalk will be devoted to the case of clustering of plumesin Rayleigh-Benard convection: through a two-scale pro-cess, kinetic energy is transferred mainly to low horizontalwave numbers while the sizes of individual plumes remainon the scale of the boundary layer thickness. Again in adirect numerical simulation framework, the study of thePrandtl problem is addressed as a simplified model of dryatmospheric convection, kept in statistically stationary ra-diativeconvective equilibrium. Finally the emergence andtemporal evolution of large-scale spatial-temporal oscillat-ing modes in deep moist convection, for an atmospherein radiative-convective equilibrium. To this end, we usecloud-resolving numerical simulations of the convective at-mosphere at very high resolution and on a very large do-main, using WRF model in LES mode.

Antonio ParodiIstituto di Scienze dell’Atmosfera e del Climaantonio.parodi@cimafoundation.org

High Rayleigh Number 2D Rayleigh-Benard Con-vection

Although there is a significant understanding of the ulti-mate regime of Rayleigh-Benard convection, there are stillsome open questions regarding the transition towards itand the logarithmic boundary layers associated with it. Wereport the results of our 2D DNS that have contributed tounderstanding the transition to the ultimate regime as wellas the encountered difficulties pushing our code towardshigh Ra.

Erwin van der Poel, Rodolfo Ostilla MonicoUniversity of Twentee.p.vanderpoel@utwente.nl, r.ostillamonico@utwente.nl

Roberto VerziccoUniversity of Romar.verzicco@utwente.nl

Detlef LohseUniversity of Twented.lohse@utwente.nl

Scalable Coupling of Surface-Subsurface WaterFlows

Recent advances in computing architectures push towardsthe development of computational codes with an optimalscaling. We have developed a coupled surface-subsurfacewater flow model that solves the governing equations withdiscontinuous Galerkin and control volume finite elementmethods. Our model uses an explicit time discretisationfor the 3D Richards equation and hence achieves optimalscaling both weakly and strongly. A wide range of testproblems have been solved to highlight the model proper-ties.

Thomas De MaetUniversite catholique de Louvainthomas.demaet@uclouvain.be

Emmanuel HanertUCLouvainEarth and Life Institute - Environmental Sciencesemmanuel.hanert@uclouvain.be

Evaporation from Porous Media Influenced by At-mospheric Processes

Evaporation from porous media into the ambient air in-volves varios interacting processes and depends on a mul-titude of properties of the fluids, of the porous mediumand of the flow regime. The evaporation rate can be lim-ited from the porous-medium side, e.g. due to limitedwater supply by capillary forces or by diffusion throughthe tortuous porous medium, or from the free-flow sideinvolving the transfer through a boundary layer. Model-ing such complex system on the scale of representative el-ementary volumes (REVs) is a challenging task. We havedeveloped a model for the coupled simulation of a two-phase porous medium flow (Darcy) and a laminar free flow(Stokes) under non-isothermal conditions. Possible exten-sions and simplifications to the developed laminar coupled

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model are discussed.

Thomas FetzerDepartment of HydromechanicsUniverity of Stuttgartthomas.fetzer@iws.uni-stuttgart.de

Klaus MosthafUniversitaet Stuttgart, IWSklaus.mosthaf@iws.uni-stuttgart.de

Transition Region Model for Coupling Free Flowand Porous Medium Systems

A transition region model for coupling single-phase two-component free flow and two-phase two-component porousmedium systems is developed by means of the thermody-namically constrained averaging theory (TCAT) approach.The model is averaged in the direction normal to theboundaries of the free flow and porous medium domainsbeing joined. Unlike sharp interface approximations, theTCAT transition region model resolves the storage andtransport of mass, momentum and energy.

Iryna RybakUniversitaet Stuttgart, IANSrybak@ians.uni-stuttgart.de

William G. GrayDepartment of Environmental Sciences and Engineering,University of North Carolina, Chapel Hillgraywg@unc.edu

Cass T. MillerUniversity of North CarolinaChapel Hillcasey miller@unc.edu

Numerical Assessment of Different Discretizationsfor Stokes-Darcy Coupling

There are a number of options in the numerical simulationof the Stokes-Darcy problem. This talk presents studies ofdifferent approaches for applying interface conditions andthe use of inf-sup stable and stabilized finite elements forthe mixed (dual) Darcy problem.

Ulrich WilbrandtFree University of BerlinDepartment of Mathematics and Computer Sciencewilbrand@wias-berlin.de

Solution of transient CSEM problems in model re-duction framework

We suggest general model reduction framework for thesolution of large scale multidimensional transient inverseproblems. Rational Krylov subspace model reduction ac-celerates the solution of the forward problem and efficientlycompresses the data in time and space. A nonlinear trans-

form of the compressed data (based on the Stieltjes-Krein-Marchenko-Gelfant-Levitan method) speeds up Gauss-Newton iterations and improves quality of inversion. Weillustrate our approach using synthetic 2.5D CSEM exam-ples of hydrocarbon reservoirs in the marine environment.

Aria AbubakarSchlumberger Doll Researchaabubakar@slb.com

Liliana BorceaRice Universityborcea@rice.edu

Vladimir L. Druskin, Tarek HabashySchlumberger-Doll Researchdruskin1@slb.com, habashy1@slb.com

Alexander MamonovUT Austin: mamonov@gmail.com

Valeria SimonciniUniversita’ di Bolognavaleria.simoncini@unibo.it

Mikhail ZaslavskySchlumberger-Doll Researchmzaslavsky@slb.com

Regularization for Nonlinear Inverse Problems

Ill-posed nonlinear inverse problems require regularized so-lutions, and typically this is done iteratively with Gauss-Newton or Levenburg-Marguart methods. The discrepancyprinciple determines regularization parameters by applyinga χ2 test, and here we will extend that idea to show thata χ2 test can be applied at each iterate of these nonlinearmethods. This test is used to estimate regularization pa-rameters for nonlinear problems, and results will be shownon benchmark problems in Geophysics.

Jodi MeadBoise State UniversityDepartment of Mathematicsjmead@boisestate.edu

Chad HammerquistSensty Group, Inc.chadhammerquist@gmail.com

3D Forward and Inverse Modeling of Geo-Electromagnetic Fields

The inversion of geo-electromagnetic data is a nonlinearand ill-posed problem. In large-scale settings it is gen-erally solved iteratively using regularized Newton, Quasi-Newton, Gauss-Newton or all-at-once approaches. The for-ward problem is demanding because of complex geometriesimposed by natural environments, the different physical be-haviors of the fields, a multitude of source configurationsand many right-hand sides. We formulate the problem inthe time and frequency domains using Nedelec finite ele-ments on unstructured grids and apply Krylov subspace

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techniques to reduce the numerical costs.

Klaus Spitzer, Ralph-Uwe BoernerInstitute of Geophysics and GeoinformaticsTU Bergakademie Freibergklaus.spitzer@geophysik.tu-freiberg.de,rub@geophysik.tu-freiberg.de

Michael EiermannTU Bergakademie FreibergInstitut fur Numerische Mathematik und Optimierungeiermann@math.tu-freiberg.de

Oliver G. ErnstTU Bergakademie FreibergFakultaet Mathematik und Informatikernst@math.tu-freiberg.de

Joint Inversion in Poroelasticty

Remote sensing and geodetic measurements are providinga wealth of new, spatially-distributed, time-series data thatpromise to improve the characterization of the subsurfaceand the monitoring of pressure transients due to fluid in-jection and production. We formulate a Bayesian inverseproblem to infer the permeability distribution in a quasi-static poroelastic model from the joint inversion of time-series surface deformation and well pressure measurements,and compare different methods to characterize the poste-rior probability density of the permeability.

Georg StadlerUniversity of Texas at Austingeorgst@ices.utexas.edu

Noemi PetraInstitute for Computational Engineering and Sciences(ICES)The University of Texas at Austinnoemi@ices.utexas.edu

Coupling Navier-Stokes and Darcy Equations:Modeling and Numerical Methods

We present two possible methods to compute the finite-elements approximation of a Navier-Stokes/Darcy prob-lem to model filtration processes through porous media.First, using suitable continuity conditions, we transformthe coupled problem into an equivalent one on the inter-face separating the fluid from the porous medium. Then,adopting an optimal-control approach, we couple the twosub-problems avoiding relying on any interface conditions.We compare these approaches theoretically and on sometest cases of physical relevance.

Marco DiscacciatiLaboratori de Calcul Numeric

Universitat Politecnica de Catalunya, Barcelona, Spainmarco.discacciati@upc.edu

Mathematical and Numerical Delicacies in CoupledOcean-atmosphere Simulations

Atmospheric and oceanic simulation models are widelyused for weather, general circulation, and climate. Inthis context, the simulated flows are spectrally broad bandacross global to micro scales. A full representation in differ-ent scales is uncomputable and numerical models containparameterizations to account for unresolved processes. Themathematical formulation of parameterization schemes isdevised empirically, and often impairs the regularity of thesolutions. This problem is even more acute when consid-ering coupled ocean-atmosphere models. In this talk, it isshowed that this complexity has to be taken into accountto devise mathematically consistent and efficient couplingalgorithms. This problem is here addressed from the pointof view of Schwarz-like domain decomposition methods.Using a hierarchy of examples, from highly simplified tofully-realistic cases, the delicacies associated with ocean-atmosphere coupling are illustrated both theoretically andnumerically.

Florian LemarieInstitute of Geophysics and Planetary PhysicsUCLA Dept ofAtmospheric and Oceanic Sciencesflorian.lemarie@inria.fr

An Overview of Coupling Strategies betweenOcean and Atmosphere in Earth System Models

Earth system models are used to study climate variabil-ity from decades to millennium. Historically, they havebeen built from several components : ocean, atmosphere,sea-ice, etc. Each component comes from a scientific com-munity. It is validated with fixed boundary conditions.Coupling consists in exchanging boundary conditions. To-benefit from the communities expertise, initial methodsminimize scientific and technical modifications in the com-ponents. This review considers existing coupling strategiesunder the constraints brought by the physics, numerics andinformatics.

Olivier MartiInstitut Pierre Simon Laplaceolivier.marti@lsce.ipsl.fr

Sophie ValckeCentreEuropeen deRecherche et deFormationAvanceeenCalcsophie.valcke@cerfacs.fr

Domain Decomposition for Poroelasticity and Elas-ticity with DG Jumps and Mortars

We couple a time-dependent poroelastic model in a regionwith an elastic model in adjacent regions. We discretizeeach model independently on non-matching grids and werealize a domain decomposition on the interface betweenthe regions by introducing DG jumps and mortars. Theunknowns are condensed on the interface, so that at eachtime step, the computation in each subdomain can be per-formed in parallel. In addition, by extrapolating the dis-

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placement, we present an algorithm where the computa-tions of the pressure and displacement are decoupled. Weshow that the matrix of the interface problem is positivedefinite and establish error estimates for this scheme.

Vivette GiraultUniversity of Paris VIgirault@ann.jussieu.fr

Gergina PenchevaUniversity of Texas at Austingergina@ices.utexas.edu

Mary F. WheelerCenter for Subsurface Modeling, ICESUniversity of Texas at Austinmfw@ices.utexas.edu

Tim WildeyOptimization and Uncertainty Quantification Dept.Sandia National Laboratoriestmwilde@sandia.gov

Comparison of DDFV and DG Methods for Flowin Anisotropic Heterogeneous Porous Media

We consider unsteady single-phase flows modeled by theRichards’ equation. We compare Discrete Duality FiniteVolume and Discontinuous Galerkin schemes applied todiscretize the diffusive term. Backward Differentiation For-mula of second order is used for the time stepping method.Accuracy and robustness of these two types of schemes aretested and compared on various test cases, especially inanisotropic heterogeneous media.

Vincent BaronUniversite de NantesLaboratoire de Mathematiques Jean Lerayvincent.baron@univ-nantes.fr

Yves CoudiereINRIAyves.coudiere@inria.fr

Pierre SochalaBRGMp.sochala@brgm.fr

Non Linear Finite Volume Schemes For the HeatEquation in 1D

Many solutions exist for the numerical approximation ofdiffusive equations on general unstrutured grids. But ifone needs high order and the preservation of the maxi-mum it becomes quite challenging. In particular the nonlinear techniques used for hyperbolic equations cannot beused without strong modifications. I will review recent ad-vances in the understanding of the mathematical and nu-merical structure of this problem: in particular I will detaila 1D example (based on multiD Le Potier’s Finite Volumeschemes) where high order (third order in practice in 1D)and preservation of the maximum principle are obtainedtogether.

Bruno DespresUniversity Paris VI

Laboratory LJLLdespres@ann.jussieu.fr

Soil Moisture Dynamics and Rain InterarrivalTimes

Soil moisture data taken down to two meters has beenused for assessing the relations between the vertical dis-cretization and rain interarrival times. A one dimensionalRichards equation solution provided the tool for also eval-uating the effects of hysteresis in the soil water retentioncurve. A statistics of soil moisture time variations can berelated to the pdf of interarrival times.

Stefano FerrarisUniversity of Turinstefano32@gmail.com

A Non Linear Correction and Maximum Principlefor Diffusion Operators with Hybrid Schemes andDiscrete Dual Finite Volume Schemes

In the framework of nuclear waste disposal simulation,we are interested in a transport model in porous mediawhich can be described by a convection-diffusion equation.Recently, nonlinear finite volume schemes have been pro-posed to discretize diffusion operators. For these meth-ods, discrete maximum principle has been obtained for dis-torted meshes or highly anisotropic diffusion tensors. Inthe present work, we extend this technique to the classof hybrid schemes and to the discrete dual finite volumemethods. We show that this correction is equivalent to theoriginal scheme with a modified flux which is consistent.We give a few words about the coercivity of the modi-fied algorithm. Finally, we show that the new method isnonoscillating. Using an analytical solution, we show therobustness and the accuracy of this algorithm in compari-son with results obtained by linear schemes which do notsatisfy the minimum principles on this test.

Christophe Le PotierCEAGif sur yvetteclepotier@cea.fr

Konstantin LipnikovLos Alamos National Laboratorylipnikov@lanl.gov

Numerical Analysis of a Smagorinsky LES Modelfor Primitive Equations

This work deals with the development of efficient numer-ical solvers for the Primitive Equations of the ocean inturbulent regime. We derive the numerical approximationof a reduced model by the Smagorinsky turbulence modelthat includes stabilization of the pressure discretization bya penalty technique. We perform the numerical analysis ofthis discretization (stability, convergence, error estimates),obtaining error estimates of at most first order in naturalnorms, due to the penalty structure of the Smagorinskyeddy viscosity. We finally perform some numerical testsfor the Primitive and Navier-Stokes equations, that con-

104 GS13 Abstracts

firm the theoretical convergence expectations.

Macarena Gomez MarmolUniversidad de Sevillamacarena@us.es

Lagrangian Tools and the Assessment of the Pre-dictive Capacity of Geophysical Data Sets

We examine, with recently developed Lagrangian tools, al-timeter data and numerical simulations obtained from theHYCOM model in the Gulf of Mexico. Our data corre-spond to the months just after the Deepwater Horizonoil spill in the year 2010. Our Lagrangian analysis pro-vides a skeleton that allows the interpretation of transportroutes over the ocean surface. The transport routes arefurther verified by the simultaneous study of the evolu-tion of several drifters launched during those months in theGulf of Mexico. We find that there exist Lagrangian struc-tures that justify the dynamics of the drifters, although theagreement depends on the quality of the data. We discussthe impact of the Lagrangian tools on the assessment ofthe predictive capacity of these data sets.

Carolina MendozaUniversidad Politecnica de MadridSpaincaromendoza@gmail.com

Ana M. ManchoInstituto de Ciencias MatematicasConsejo Superior Investigaciones CientificasA.M.Mancho@icmat.es

Denny KirwanUniversity of Delawareadk@udel.edu

Stephen WigginsUniversity of Bristols.wiggins@bristol.ac.uk

Grand LAgrangian Deployment (GLAD): OptimalLaunch Strategies for Dispersion Near the Deep-water Horizon Oil Spill Site

Initial dispersion, residence time, and advective pathwayresults obtained from the nearly simultaneous deploymentof some 300 surface drifters in the vicinity of the DwHoil spill in the DeSoto Canyon are reported. The goal ofthe GLAD experiment was to characterize, with unprece-dented statistical significance, multi-point and multi-scaledispersion properties of the flow in the region of the DwHspill site including demarcation of the advective pathwaysbetween the Canyon and larger-scale flow features in theGulf. GLAD was designed and executed to consist of op-timal launch templates needed for dispersion calculations.For the initial time period considered, drifter motion wascharacterized by large amplitude inertial motions, over-all strong topographic control, and significant indicationsof interior control by frontal dynamics on 1-5 km scales.Very limited exchange, either across-shelf or with nearbymesoscale features, was observed and residence times in theCanyon typically exceeded one week with many drifters re-maining there for more than 21 days.

Tamay Ozgokmen

University of Miami/RSMAStozgokmen@rsmas.miami.edu

Andrew PojeCUNY / College of Staten Islandandrewpoje@gmail.com

Bruce LipphardtSMSP, University of Delaware, Newark DE 19716brucel@udel.edu

Brian HausUniversity of Miamibhaus@rsmas.miami.edu

Gregg JacobsNRLgregg.jacobs@nrlssc.navy.mil

M. Josefina Olascoaga, Edward Ryan, Guillaume NovelliUniversity of Miamijolascoaga@rsmas.miami.edu, eryan@rsmas.miami.edu,gnovelli@rsmas.miami.edu

Angelique C. HazaRSMAS, University of Miamiahaza@rsmas.miami.edu

Denny Kirwan, Jr.University of Delawareadk@udel.edu

Multi-Phase Air-Sea Interface Model

We have implemented a model of the air-sea and air-oilinterface with surface tension using a VOF multi-phaseCFD model. Under hurricane conditions, the interface wasdisrupted by Kelvin-Helmholtz instability, forming two-phase transition layer. Experiments with imposed shortwavelets revealed streamwise coherent structures and tear-ing of wave crests, formation of water sheets and spume.The numerical simulation provided an estimate for the gasphase hydrocarbons flux from the ocean to the atmosphereunder hurricane conditions.

Alex SolovievOceanographic CenterNova Southeastern Universitysoloviev@nova.edu

The Search for Lagrangian Coherent Structures inCoastal Areas: Results from the Gelato 2012 Ex-periment in the Gulf of Naples

Enrico ZambianchiDepartment of Science and TechnologyParthenope University, Napoli, Italenrico.zambianchi@uniparthenope.it

Absolute and Relative Permeability for Water-wetSystems Calculated in the Presence of Micro- (un-

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resolved) Porosity

Christoph ArnsSchool of Petroleum EngineeringThe University of New South Walesc.arns@unsw.edu.au

Pore Geometry: Film Menisci Motion and Throats

We discuss two related problems in the motion of fluidsthrough porous media. The first is the motion of thearc-menisci governing wetting films in channel cross sec-tions. In the second we address the question ”what is athroat” and demonstrate the importance of this questiononce porosity rises above 20%.

W. Brent LindquistApplied Mathematics and Statistics, Stony BrookUniversityb.lindquist@stonybrook.edu

Daesang KimApplied Mathematics and StatisticsStony Brook Universitydaesang.kim@stonybrook.edu

Joo-Won KimStony Brook Universityjwkim@stonybrook.edu

Pore Scale Coupling of Fluid and Solid Mechan-ics for Simulation of Infiltration of Fines in PorousMedia

Due to heterogeneity, standard constitutive relationshipsand models yield poor predictions for flow and rock prop-erties of the porous media infiltrated by fines. We couplecomputational fluid dynamics and discrete element model-ing to simulate the particulate flow through porous me-dia. Pore scale simulations allow for visualization andunderstanding of clogging processes while varying parti-cle/grain size ratio, fluid viscosity, flow rate and poros-ity. Further, velocity fields are integrated into a distinctlynon-monotonic permeability-porosity/(depth of penetra-tion) relationship.

Masa Prodanovic, Maryam MirabolgUniversity of Texas at AustinDepartment of Petroleum and Geosystems Engineeringmasha@ices.utexas.edu, maryam@ices.utexas.edu

Hybrid Multiscale Finite Volume Method for Two-Phase Flow trough Porous Media

We present a hybrid multiscale algorithm that couplesDarcy- and pore-scale descriptions of two-phase flowtrough porous media. The Darcy-scale problem is formu-lated using the Multiscale Finite Volume method, whichallows adaptive reconstruction of fine-scale details. At porescale we solve the Navier-Stokes equations in combinationwith Volume Of Fluid method. The results of the hybridsimulations are compared with direct pore-scale solutionsfor several flow regimes and the limits of Darcy’s law are

discussed.

Pavel TominPremier Assistant (Postdoc)University of Lausannepavel.tomin@unil.ch

Pavel TominPhD StudentMIPTpavel.tomin@unil.ch

Volume of Fluid Direct Numerical Simulations ofInvasion of 3D porous media

We shall present the Volume of Fluid method with theheight function method for surface tension, and discusscontact angle implementations in the Gerris Flow Solvercode. Then we show some example direct numerical sim-ulations solving the Navier-Stokes equations in 3D porousmedia on a parallel architecture. We discuss accuracy andscalability issues.

Stephane ZaleskiUniversite Pierre et Marie Curiestephane.zaleski@upmc.fr

Igor BondinoGeoccience Research Centre, Total E&P UKigor.bondino@total.com

Bertrand LagreeUniversite Pierre et Marie CurieTotallagree@dalembert.upmc.fr

A Finite Element Optimization Method for Simu-lating Discrete Fracture Network Flows

We investigate a new numerical approach for the computa-tion of 3D flows in a discrete fracture network that does notrequire conforming discretization of PDEs on complex 3Dsystems of planar fractures. The discretization within eachfracture is performed independently of the discretization ofthe other fractures and of their intersections. Independentmeshing process within each fracture is a very importantissue for large scale simulations, making easier mesh gen-eration. Simulations will be shown to prove the viabilityof the method. The resulting approach can be naturallyparallelized for dealing with systems with a huge numberof fractures.

Stefano BerronePolitecnico di Torinosberrone@calvino.polito.it

Sandra PieracciniDipartimento di MatematicaPolitecnico di Torino, Italysandra.pieraccini@polito.it

Stefano Scialo‘

106 GS13 Abstracts

Politecnico di TorinoDipartimento di Scienze Matematichestefano.scialo@polito.it

Coupled Flow Model and Simulation in 3D Porous-fractured Media

Taking into account water and solute exchanges betweenporous and fractured media is of great interest in geologicalapplications. The coupled porous-fractured flow equationsand their discretization by a Mixed Hybrid Finite ElementMethod are presented as well as the derived linear system.An appropriate mesh generation is proposed to deal withthe complexity involved by randomly generated fracturenetworks. Numerical experiments are shown, that provideflow fields for forthcoming transport simulations.

Thomas DufaudINRIA-Rennes, Francethomas.dufaud@inria.fr

Jocelyne ErhelINRIA-Rennes, FranceCampus de BeaulieuJocelyne.Erhel@inria.fr

Geraldine PichotINRIA-Rennes, FranceCampus de Beaulieugeraldine.pichot@inria.fr

Reduced Models for Flow in Networks of Fractures

Subsurface flow is influenced by the presence of faults andlarge fractures which act as preferential paths or barriers.Several models have been proposed to handle fractures in aporous medium as objects of co-dimension 1. In this workwe consider the case of a network of intersecting fractures,with the aim of deriving physically consistent and effectivecoupling conditions at the intersection between fractures.This new model accounts for the angle between fracturesat the intersections and allows for jumps of pressure acrossthe intersection. This permits to describe the flow more ac-curately than models that impose pressure continuity whenfractures have different properties. The main mathematicalproperties of the model are analysed. We consider a numer-ical discretisation where fractures may be non-matching atthe intersection to increase the flexibility of the methodin the case of complex geometries characterized by a highnumber of fractures.

Luca FormaggiaDepartment of MathematicsPolitecnico di Milano, Italyluca.formaggia@polimi.it

Alessio FumagalliMOX, Department of MathematicsPolitecnico di Milano, Italyalessio.fumagalli@mail.polimi.it

Anna ScottiPolitecnico di Milanoanna.scotti@mail.polimi.it

DFM Modelling for Non-Matching Fracture andMatrix Grids: Pressure Continuity and BoundaryConditions

Fractured porous-media systems are simulated, where thecharacteristic flow behavior depends on both the fracturesand the matrix. A structured rock-matrix grid is cou-pled with an independent, arbitrarily orientated fracture-network grid of codimension one that leads to discontin-uous solutions across the fractures which are handled byan XFEM approach. Discontinuities also occur at fracturecrossings. A consistency condition which can handle arbi-trary crossings is presented as well as consistent boundaryconditions for fractured boundaries.

Nicolas SchwenckUniversity of StuttgartNicolas.Schwenck@iws.uni-stuttgart.de

Barbara WohlmuthTechnical University of Munichbarbara.wohlmuth@ma.tum.de

Helmig RainerUniversity of Stuttgartrainer.helmig@iws.uni-stuttgart.de

A Multiscale Model for Network Flow Embeddedin Porous Media

In this talk, we consider the coupling between two diffusion-reaction problems and two transport equations, one definedin a three-dimensional domain Ω ⊂ R3, the other in a one-dimensional subdomain Λ ⊂ Ω, respectively. The math-ematical analysis of such problems must be handled withcare, because the coupling between Λ and Ω is establishedby measure terms. Finally we describe, how this modelcan provide the basis for a multiscale analysis of processesoccuring in the context with natural gas production by hy-draulic fracturing.

Barbara WohlmuthM2, Centre for Mathematical Sciences,Technische Universitat Munchen, Germanywohlmuth@ma.tum.de

Tobias KopplTechnische Universitat Munchen, Germanykoeppl@ma.tum.de

An Efficient Numerical Method for ASP Floodingin Tertiary Oil Recovery

In this talk, we present a new efficient, high order accuratehigh performance numerical method for solving a coupledhighly nonlinear system of partial differential equationsarising in the context of the fractional flow model of Alkali-Surfactant-Polymer flooding of oil reservoirs. The methodis based on the use of an extended FEM elliptic solver, animplicit-time linearized FDM, and level set formulation.We will present numerical results using this method. The

GS13 Abstracts 107

research reported here has been made possible by a grant(NPRP 08-777-1-141) from the Qatar National ResearchFund (a member of The Qatar Foundation). The state-ments made herein are solely responsibility of the authors.

Sourav DuttaTexas A&M Universitysdutta@math.tamu.edu

A Mixed Approach ”Pore-Network Model/DirectNumerical Simulation” to Simulate MultiphaseFlow Processes

Many petroleum or chemical engineering processes involvemultiphase flows in porous media with interface dynamicspreventing the use of classical quasi-static network models.We develop mixed models involving two distinct modeliza-tions : a classical pore-network approach, coupled locally,whenever this is required by the flow dynamics, to a mul-tiphase solver (VOF). The continuous dialog between bothmodelizations required the introduction of an innovativepenalization method for solving two-phase flows over com-plex geometries on simple Cartesian meshes.

Pierre HorgueInstitut de Mecanique de Fluides de Toulousepierre.horgue@imft.fr

Michel Quintard, Marc PratInstitut de Mecanique des Fluides de Toulousemichel.quintard@imft.fr, marc.prat@imft.fr

Scale Analysis of Miscible Density-Driven Convec-tion in Porous Media

Scale analysis of unstable density-driven miscible convec-tion in porous media reveals that both concentration vari-ance production and dissipation rates are independent ofthe Rayleigh number (beyond a critical limit). As a con-clusion, ensemble averaged Darcy modeling and the large-mode simulation approach are proposed to compute thebehavior after a short onset time. The former method tar-gets ensemble averaged solutions and the latter coarse scalefinger dynamics; in both cases a dramatic reduction of com-putational cost is achieved.

Joohwa LeeAUDI AGjoohwa0207@googlemail.com

Optimal Flux Allocation and Control of VolumeErrors in Streamline-Based Flow Simulation

Advection dominated porous media flow can be solved ef-ficiently by transporting components along a time-varyingstreamline grid and accounting for non-advective transporton the underlying Eulerian grid using operator splitting. Inthis work, we investigate the flux allocation to individualstreamlines and the resulting volume errors between thestreamline and Eulerian grids. We present a frameworkfor balancing these errors using optimization strategies in-volving the number of streamlines and distribution of wellfluxes to streamlines.

Anna NissenEnergy Resources EngineeringStanford Universityamnissen@stanford.edu

Marco ThieleStreamsim Technologies/Stanford Universitythiele@streamsim.com

Margot GerritsenDept of Petroleum EngineeringStanford Universitymargot.gerritsen@stanford.edu

Gunilla KreissDivision of Scientific ComputingUppsala Universitygunilla.kreiss@it.uu.se

Finite Elements for Reactive Flow in a Fractureand Reaction-induced Boundary Movement

We study the reactive flow in a thin strip where the geom-etry changes take place due to reactions. Specifically, weconsider precipitation dissolution processes taking place atthe lateral boundaries of the strip. The geometry changesdepend on the concentration of the solute in the bulk (traceof the concentration) which makes the problem a free-moving boundary problem. The numerical computationsare challenging in view of the nonlinearities in the descrip-tion of the reaction rates. In addition to this, the movementof the boundary depends on the unknown concentration(and hence part of the solution) and the computation ofthe coupled model remains a delicate issue. Our aim is todevelop appropriate numerical techniques for the compu-tation of the solutions of the coupled convection-diffusionequation and equation describing the geometry changes.The performance is demonstrated with the help of numer-ical tests.

Thomas WickInstitute for Computational Engineering and SciencesThe University of Texas at Austintwick@ices.utexas.edu

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

Kundan KumarCenter for Subsurface Modeling, ICES University ofTexas at

108 GS13 Abstracts

kkumar@ices.utexas.edu

Dispersion Analysis by Rayleigh Quotients: An Ef-ficient Tool for High Order Finite Element Analysisin Wave Modeling

Dispersion analysis is a very important tool for assessingthe accuracy range of numerical methods for wave prop-agation simulations. For high order schemes, as in thecase of spectral elements, the standard dispersion analysiscan be difficult and computationally very intensive, hence amore efficient approach would be desirable. In this work wereview the Rayleigh quotient approximation of the eigen-value problem that characterizes the numerical dispersionof spectral element methods for wave propagation prob-lems in homogeneous media and extend this analysis toone-dimensional, periodic layered media in the particularcase where the ratio between the wavelength and the layerthickness is high. This regime is relevant for interpretingstratigraphic data. In addition to spectral element meth-ods, we study the numerical dispersion of a poly-grid spec-tral element method in which the velocity field is writtenin terms of Haar wavelet functions within each element.

Saulo P. OliveiraUniversidade da Bahiasaulopo@ufpr.br

Saulo P. OliveiraUniversidade Federal do Paranasaulopo@ufpr.br

Geza SerianiIstituto Nazionale di Oceanografia edi Geofisica Sperimentalegseriani@ogs.trieste.it

Seismic Wave Propagation and Earthquake Sim-ulations Based on a 3D Fourier Pseudo-spectralMethod

We have recently implemented the Fourier pseudo-spectralmethod (FPSM) into a numerical code for effective largescale 3D modelling of seismic wave propagation and earth-quake simulation on highly parallel computers. In particu-lar, the new code uses vertically stretched staggered grids,and it includes features such as general intrinsic attenu-ation of the medium, anisotropy, irregular surface topog-raphy and extended earthquake sources, with kinematicrupture description. We present the main code featuresand some recent application results.

Enrico PrioloNational Institute of Oceanography and ExperimentalGeophysiOGS-Triesteepriolo@inogs.it

Peter KlinNational Institute of Oceanography and ExperimentalGeophys.OGS - Triestepklin@inogs.it

Lessons Learnt from Recent Earthquakes: the Im-

portance of 3D Physical Modeling in Insurance andReinsurace Market

The recent earthquake sequences that hit New Zealand(Sep. 2010-Dec. 2011, Canterbury plain) and NorthernItaly (May 2012, Emilia-Romagna), proved once more thata detailed description of the seismic scenario is required.We will present a challenging case study, aiming at simu-lating the seismic response of the central business district(CBD) of Christchurch, located in the alluvial plain of Can-terbury in New Zealand. The Canterbury sequence caused181 casualties and devastated the entire region. We de-cided to focus on the Lyttleton event event, modeling thekinematic rupture along the fault and studying the wavepropagation through the complex deep soft-soil sedimentsup to the high and middle rise buildings located inside theCBD of Christchurch.

Marco StupazziniMunich REmstupazzini@munichre.com

Roberto GuidottiDipartimento di Ingegneria StrutturalePolitecnico di Milanoguidotti@stru.polimi.it

Ilario MazzieriPolitecnico di Milanoilario.mazzieri@mail.polimi.it

Chiara SmerziniDipartimento di Ingegneria StrutturalePolitecnico di Milanocsmerzini@stru.polimi.it

Modeling Biot Systems in Porous Media

In this paper we consider modeling complex processes inporous media taking into account fluid motion and ac-companying solid deformations. Important applicationsin environmental engineering and petroleum engineeringinclude carbon sequestration, surface subsidence, pore col-lapse, cavity generation, hydraulic fracturing, thermal frac-turing, wellbore collapse, sand production, fault activa-tion, and waste disposal. Here we employ a multipointflux mixed finite element method for modeling Darcy flowand a continuous Galerkin method for elasticity. This Biotsystem is decoupled using a fixed stress iterative couplingscheme. We present both theoretical and computationalresults demonstrating convergence of this approach as wellas efficiency in parallel implementation. Specific treatmentof discrete fractures, effects of stress dependent permeabil-ity, and multiphase flow are discussed.

Andro MikelicInstitut Camille Jordan, Departement de MathematiquesUniversite Lyon 1Andro.Mikelic@univ-lyon1.fr

Bin WangCenter for Subsurface Modeling, ICESThe University of Texas at Austin

GS13 Abstracts 109

binwang@ices.utexas.edu

A Comparison of Explicit Continuous and Discon-tinuous Galerkin Methods and Finite Differencesfor Wave Propagation in 3D Heterogeneous Media

Traditionally, the wave equation is solved in the time do-main with the finite-difference method because of the rel-ative ease of coding and parallelization, the use of high-order spatial discretization schemes and its computationalspeed. However, finite elements on tetrahedral meshes aremore flexible and accurate, if the mesh follows the geome-try of the impedance contrasts and of the surface topogra-phy. We compare the DG symmetric interior penalty andcontinuous mass-lumped finite elements with finite differ-ences. The results show that for simple models the finitedifferences outperform finite element method by at least anorder of magnitude. For a model with interior complexityand topography, the finite elements are about two ordersof magnitude faster than finite differences. As applicationswe consider seismic modeling and migration.

Elena Zhebel, Sara MinisiniShell Global Solutions Internationalelena.zhebel@shell.com, sara.minisini@shell.com

Alexey KononovSource Contracting BValexey.kononov@shell.com

Wim A. MulderShell Global Solutions InternationalDelft University of Technologywim.mulder@shell.com

An Adaptive Multiscale Finite Element Method

We discuss and introduce an adaptive multiscale finite ele-ment method (MsFEM) for solving elliptic problems withrapidly oscillating coefficients. Starting from a general ver-sion of the MsFEM with oversampling, we present an aposteriori estimate for the H1-error between the exact so-lution of the problem and a corresponding MsFEM approx-imation. Our estimate holds without any assumptions onscale separation or on the type of the heterogeneity. Theestimator splits into different contributions which accountfor the coarse grid error, the fine grid error and even theoversampling error. Based on the error estimate we con-struct an adaptive algorithm that is validated in numericalexperiments.

Patrick HenningUniversity of Munster,Institut fur Numerische und Angewandte Mathematikpatrick.henning@uni-muenster.de

Mario OhlbergerUniversitat MunsterInstitut fur Numerische und Angewandte Mathematikmario.ohlberger@uni-muenster.de

Ben SchweizerTU DortmundFakultat fur Mathematikben.schweizer@tu-dortmund.de

TOF-based two-phase Upscaling of Flow andTransport in Subsurface Formations

Flow and transport in subsurface formations are affectedby geological variability over multiple length scales. Inthis talk, we present a TOF-based two-phase upscalingapproach to generate upscaled two-phase flow functions.This approach uses more accurate local saturation bound-ary conditions, which are found to have a dominant impact(in comparison to the pressure boundary conditions) on theupscaled two-phase flow models. It incorporates single-phase flow and transport information into local upscalingcalculations, effectively account for the global flow effects,as well as the local variations due to subgrid heterogeneity.The method was applied to permeability fields with differ-ent correlation lengths and various fluid-mobility ratios. Itwas shown that the new method consistently outperformsexisting local two-phase upscaling techniques and providesaccurate coarse-scale models for both flow and transport.

Yan LiChevronsdyanli@gmail.com

Yuguang ChenChevron Energy Technology CompanyYChen@chevron.com

Multiscale Finite Volume Method As a Frameworkfor Physically Motivated Model Reduction.

In subsurface flow simulations, multiscale methods havebeen developed as tools to improve computational effi-ciency. Some of them, however, offer an excellent frame-work to combine several physical descriptions at differentscales and in different regions. By using the Multiscale Fi-nite Volume method, we discuss the possibility of choosingadaptive coarsening criteria based on physical considera-tions. We show application to flow through porous media,with special attention to applications involving interfacedynamics at the pore scale.

Pavel TominPremier Assistant (Postdoc)University of Lausannepavel.tomin@unil.ch

Pavel TominPhD StudentMIPTpavel.tomin@unil.ch

Reduced Modeling by Global Transmissibility Up-scaling for Optimzation

Reservoir models are often too detailed for optimization

110 GS13 Abstracts

purposes. We present a framework for automatic modelreduction using global information that consists of threecomponents: algorithms to coarsen the grid, transmissibil-ity upscaling methods, and a robust fully implicit solver.Through a combination of these methods, one can incor-porate the most important reservoir responses for use inoptimization. In particular, we discuss different ways ofusing global information to partition the grid and upscaletransmissibilities.

Halvor M. NilsenSINTEFOslohnil@sintef.no

Stein KrogstadSINTEF ICTStein.Krogstad@sintef.no

An Approximate Method for Multiphase Scale-Up

Coarsening and upscaling are common practices in reser-voir simulation for reducing model size to improve com-putational efficiency. As part of the standard simulationworkflow, engineers upscale geological models to simulationmodels to speed up the run and at the same time reducethe requirement on resources, e.g., memory. Coarseningis also an attractive approach for reduced order modeling.In that case, aggressive coarsening is carried out to dras-tically reduce the size of the simulation model, and hencesimulation time. Reduced order modeling plays a crucialrole in uncertainty quantification, history match, and otherapplications where a large number of simulation runs arerequired. This presentation describes a new method for up-scaling relative permeability for the purpose of multiphaseflow simulation. This method is simple, efficient, and treatsphysics factors important to recovery processes. With thisapproach, approximations are introduced to eliminate theneed for local or global multiphase flow simulations for thepurpose of building coarse-scale displacement tables (pseu-dos). Instead, the technique is based on global pressure so-lutions and velocity fields for incompressible single phaseflow. Using the velocity fields, time-of-flight (TOF) andsaturation distributions are obtained by solving finite dif-ference equations using a sequential procedure. For testing,coarse-scale relative permeability tables are used to simu-late flow on fields with challenging horizontal and verticalpermeability properties. Test results show that the use ofthe proposed multiphase upscaling method preserves accu-racy of simulation on the coarse scale, while speeding upthe run by more than 100 times.

Yahan Yang, Xiaochen WangExxonMobilyahan.yang@exxonmobil.com.,xiaochen.wang@exxonmobil.com

Xiao-Hui Wu, Linfeng BiExxonMobil Upstream Research Companyxiao-hui.wu@exxonmobil.com, linfeng.bi@exxonmobil.com

Dynamic Simulation of Tsunamigenic EarthquakeRupture

Earthquakes might generate disproportionately largetsunamis due to particular characteristics that include slowrupture speed, rupture up to the trench and slip on splayfaults. I will summarize current results from models of sub-duction earthquake cycle and dynamic rupture aimed atunderstanding which physical properties of the subductionmegathrust can lead to such tsunamigenic earthquakes. Inparticular, I will examine the conditions that control theoccurrence of large slip and slow rupture at shallow depth.

Jean Paul AmpueroCalifornia Institute of TechnologySeismological Laboratoryampuero@gps.caltech.edu

A 3D Dynamic Rupture and See Floor Displace-ment Simulations of the 2011 Mw9 Tohoku Earth-quake

We perform earthquakes dynamic rupture simulations of2011 Mw9 Tohoku event governed by the slip weakeningfriction. Based on these simulations, we investigate thespatio-temporal evolution of the ground motion displace-ment of the see floor. Moreover, we investigate the roleof the non-planar fault of the subduction interface and itseffect on the ground motion displacement of the see floor,that in turn provide important insights on tsunamis gen-erations.

Percy Galvez

Swiss Seismological Service (SED)ETH Zurichpercy.galvez@sed.ethz.ch

Luis DalguerSwiss Seismological Service, ETH ZurichSonneggstrasse 5, CH-8092 Zurich, Switzerlanddalguer@sed.ethz.ch

Broadband Ground-Motion Simulations from Rup-ture Dynamics

Broadband ground-motion calculations for earthquake en-gineering applications are a key challenge in seismology.In this talk, I present physics-based earthquake shak-ing simulations based on dynamic rupture computationscombined with seismic scattering in heterogeneous Earth.I discuss our rupture-dynamics modeling strategy, usingcorrelated-random initial stress that generates realisticspace-time rupture evolutions. We combine the resultingband-limited synthetic seismograms with multiply S-to-Sscattered high-frequency seismic waves. I also introducesimplified rupture-modeling strategies for tsunami predic-tion.

Luis DalguerSwiss Seismological Service, ETH ZurichSonneggstrasse 5, CH-8092 Zurich, Switzerland

GS13 Abstracts 111

dalguer@sed.ethz.ch

Recent Advances in Numerical Simulation ofEarthquake Rupture Dynamics: Application to the2011 Tohoku-Ori Earthquake

Recent advances in numerical simulation of earthquakerupture dynamics using non-smooth Spectral ElementMethod are discussed here in the light of canonical prob-lems and of the recent 2011 Tohoku-ori earthquake. High-order Spectral Element approximation, combined with ex-plicit second-order time stepping, allows to simulate veryaccurately the rupture radiation in complex geological me-dia. Dynamic earthquake rupture along preexisting faultsof complex geometry is modeled as a frictional instabilityusing extension of a Barenblat-type surface energy formu-lated in terms of a slip-weakening friction law. The fric-tional contact is implemented using an implicit non-smoothcontact formalism and solved locally using Moreau’s sweep-ing process. The frictional contact is regularized to takeinto account bi-material interfaces. Simulations of the in-teraction between rupture propagation and free surface willbe in particular discussed in the light of the implicationsfor tsunami source generation.

Jean-Pierre VilotteInstitut de Physique du Globe de ParisCNRS - UMR 7154vilotte@ipgp.fr

Gaetano FestaUniversita di Napoli, Frederico IIfesta@na.infn.it

On the Regularity of Non-Negative Solutions to aLogarithmically Singular Equation

The local behaviour of solutions to a logarithmically singu-lar diffusion equation is investigated in some open space-time domain E × (0, T ]. It is shown that if at some timelevel to ∈ (0, T ] and some point xo ∈ E the solutionu(·, to) is not identically zero in a neighborhood of xo, ina measure-theoretical sense, then it is strictly positive ina proper cylindrical neighborhood of (xo, to). As a conse-quence, solutions are analytic in the space variables and atleast Lipschitz continuous in the time variable.

Ugo GianazzaDepartment of MathematicsUniversity of Paviagianazza@math.unifi.it

Structural Stability Problems for Nonlinear PDEsof Porous Media

The problems of structural stability and continuous depen-dence on initial data for Brinkman Forchheimer Equationsand related systems of equations of porous media will bediscussed

Varga KalantarovKoc University, IstanbulTurkeyvkalantarov@ku.edu.tr

On the Development and Generalizations ofCahn–Hilliard Equations within a ThermodynamicFramework

We provide a thermodynamic basis for the development ofmodels that are usually referred to as phase-field modelsfor compressible, incompressible, and quasi-incompressiblefluids. Using the theory of mixtures as a starting point,we develop a framework within which we can derive phase-field models both for mixtures of two constituents and formixtures of arbitrarily many fluids. In order to obtain theconstitutive equations, we appeal to the requirement thatamong all admissible constitutive relations that which isappropriate maximizes the rate of entropy production (seeRajagopal and Srinivasa in Proc R Soc Lond A 460:631–651, 2004). The procedure has the advantage that thetheory is based on prescribing the constitutive equationsfor only two scalars: the entropy and the entropy pro-duction. Unlike the assumption made in the case of theNavier-Stokes-Fourier fluids, we suppose that the entropyis not only a function of the internal energy and the densitybut also of gradients of the partial densities or the concen-tration gradients. The form for the rate of entropy pro-duction is the same as that for the Navier-Stokes-Fourierfluid. As observed earlier in Heida and Malek (Int J Eng Sci48(11):1313–1324, 2010), it turns out that the dependenceof the rate of entropy production on the thermodynamicalfluxes is crucial. The resulting equations are of the Cahn-Hilliard-Navier-Stokes type and can be expressed both interms of density gradients or concentration gradients. Asparticular cases, we will obtain the Cahn-Hilliard-Navier-Stokes system as well as the Korteweg equation. Comparedto earlier approaches, our methodology has the advantagethat it directly takes into account the rate of entropy pro-duction and can take into consideration any constitutiveassumption for the internal energy (or entropy).

Josef MalekCharles University, PragueMathematical Institutemalek@karlin.mff.cuni.cz

Combined Finite Volume-Finite Element Schemefor Compressible Two Phase Flow in Porous Media

We present an industrial scheme, to simulate the two com-pressible phase flow in porous media. For homogeneous andisotropic diffusion tensor, this scheme consists in an im-plicit finite volume method together with a phase-by-phaseupstream scheme which satisfies industrial constraints ofrobustness. We show that the proposed scheme satisfy themaximum principle for the saturation and a discrete energyestimate on the velocity of each phase. For inhomogeneousand anisotropic diffusion tensor, we discretize the diffusionterm over an unstructured mesh of the space domain bymeans of the piecewise linear nonconforming finite elementmethod combined with an upwind scheme for the mobilityof each phase. We prove the convergence of the scheme,only supposing the shape regularity condition for the orig-inal mesh.We use a priori estimates and the Kolmogorovcompactness theorem for this purpose. In addition, wepresent some numerical tests in 2D on an unstructuredmesh for water-gas flows in porous media.

Mazen SaadEcole Centrale de Nantesmazen.saad@ec-nantes.fr

112 GS13 Abstracts

Towards Large-Scale Compositional Simulation ofCO2 Enhanced Oil Recovery (EOR)

This talk will focus on the simulation of CO2 EOR, and dis-cuss simulation performance (accuracy and efficiency) forvarious techniques. The impact of model complexity (e.g.,reservoir heterogeneity, relative permeability, and misciblevs. near-miscible displacements) is illustrated, and we dis-cuss the use of upscaling to speed up the simulation. It isshown that the combined use of parallel simulation, Adap-tive Implicit (AIM) models, and upscaling makes it possiblefor large-scale simulation of CO2 EOR.

Yuguang Chen, Dengen ZhouChevron Energy Technology CompanyYChen@chevron.com, dengenzhou@chevron.com

Huanquan PanDepartment of Energy Resources EngineeringStanford Universityhqpan@stanford.edu

A Multi-Physics Approach to Model Composi-tional Flow on Adaptive Grids.

A multi-physics approach is presented that reduces the nu-merical model complexity locally in an adaptive manner tolower the computational efforts per cell. This approach iscombined with adaptive refinement of the grid that usesa multi-point flux approximation in combination with thestandard two- point flux stencil. The combination of bothapproaches allows for an efficient simulation of composi-tional multi-phase flow, such as a large-scale scenario ofCO2 storage.

Benjamin FaigleUniversity of Stuttgartbenjamin.faigle@iws.uni-stuttgart.de

Ivar AavatsmarkCIPR University of Bergenivar.aavatsmark@uni.no

Application of Saturation Functions and Implica-tion of Representing Complex Dynamical Systemsin Up-Scaled Models

Compositional reservoir simulations of gas displacementprocesses incorporating complex phase behavior and dy-namic movements of phases will be presented. Basedon consistent handling of two-phase saturation functionsto three-phase conditions, examples of Water-Alternating-Gas (WAG) injection will be illustrated in 1D and 2Dmodels. Saturation history development for immiscibleand miscible WAG injection processes in a 2D troughcross stratified sandstone model at mesoscopic scale het-

erogeneities will be demonstrated. Important issues forup-scaling will be addressed.

Odd Steve HustadStatoilosh@statoil.com

Accurate and Efficient Modeling of Near-MiscibleGas Injection at Reservoir Scale

In this presentation I will focus on important aspects of anear-miscible gas injection simulation. That will includeefficiency of thermodynamic computations, accurate phasestate identification, important details of nonlinear formu-lations and nonlinear solvers. Development of miscibilityand its accurate treatment in a compositional simulation aswell as possible scaling strategies for gas injection processeswill be also discussed.

Denis VoskovEnergy Resources Engineering DepartmentStanford Univeristydvoskov@stanford.edu

Combing Models of Ice Dynamics and SubglacialHydrology

I will present recent attempts to model hydrologically con-trolled acceleration and deceleration of ice-sheets. In par-ticular, I will described a coupled model in which ice defor-mation is described with a vertically integrated model in-corporating large amounts of basal slip, and the subglacialdrainage system is described by a water sheet of variablethickness. The model will be forced by a prescribed rateof melting of the ice surface, the meltwater being routedthrough the drainage system and causing variation in basalslip as a result. I will explore and discuss different waysof describing the evolution of the drainage system and ofcoupling the drainage system to ice flow.

Ian HewittMathematics Department, University of British ColumbiaVancouver, Canadahewitt@math.ubc.ca

Discretization and Solvers for the Stokes Equationsof Ice Sheet Dynamics at Continental Scale

Ice sheets exhibit incompressible creeping flow with shear-thinning rheology. On a continental scale, the flow is char-acterized by localized regions of fast flow that are sepa-rated from vast slow regions by thin transition zones. Weuse a parallel, adaptive mesh, higher-order finite elementdiscretization to model in 3D the equations for ice sheetdynamics on a continental scale. We will address issuesrelated to the scalable solution of the resulting equations,with emphasis on the nonlinear rheology and addressingthe effects of a highly anisotropic discretization.

Tobin Isaac, Georg StadlerUniversity of Texas at Austintisaac@ices.utexas.edu, georgst@ices.utexas.edu

GS13 Abstracts 113

Advances in Ice-Sheets Simulations, Models Com-parison and Parameters Estimation

Several models of different complexity and accuracy havebeen proposed for describing ice-sheet dynamics. We intro-duce a parallel, finite element framework for implementingthese models, which range from the ”shallow ice approxi-mation” up through nonlinear Stokes flow. These modelsmake up the land ice dynamical core of FELIX, which is be-ing developed under the Community Ice Sheet Model. Wepresent results from large-scale simulations of the Green-land ice-sheet, compare models of differing complexity andaccuracy, and explore different solution methods for theresulting linear and nonlinear systems. We also addressthe problem of finding an optimal initial state for Green-land ice-sheet via estimating the spatially varying linear-friction coefficient at the ice-bedrock interface. The prob-lem, which consists of minimizing the mismatch betweena specified and computed surface mass balance and/or themismatch between observed and modeled surface veloci-ties, is solved as an optimal control problem constrainedby the governing model equations.

Matthew HoffmanLos Alamos National Laboratory, Los Alamos, NM, USAmhoffman@lanl.gov

Mauro PeregoFlorida State Universitymperego@fsu.edu

Stephen PriceLos Alamos National Laboratorysprice@lanl.gov

Andrew SalingerApplied Computational Methods Dept, Sandia NationalLabsSandia National Labsagsalin@sandia.gov

Modeling the Response of Pine Island Glacier,West Antarctica, for the next 50 years

Pine Island Glacier experienced spectacular changes overthe past decades, which are attributed to warmer oceanwaters in the Amundsen Sea affecting the floating part ofPine Island. We use ISSM and a three-dimensional higher-order model to simulate the evolution of the glacier for thenext fifty years and assess the effect of changes in severalclimate forcings and model parameters, namely basal melt-ing under the floating part, ice front position, atmosphericconditions and grounding line retreat, on ice dynamics.

Helene SeroussiJet Propulsion Laboratoryhelene.seroussi@jpl.nasa.gov

Mathieu MorlighemUniversity of California - Irvinemathieu.morlighem@jpl.nasa.goc

Eric RignotUniversity of California - IrvineJet Propulsion Laboratory - Caltecheric.j.rignot@jpl.nasa.gov

Jeremie MouginotUniversity of California - Irvinejmougino@uci.edu

Eric Larour, Ala KhazendarJet Propulsion Laboratoryeric.larour@jpl.nasa.gov, ala.khazendar@jpl.nasa.gov

A Mixed Order Scheme for the Shallow WaterEquations

Learn how to use mixed order schemes for faster simulationof the shallow water equations. This session will explainhow the use of different order schemes within the same sim-ulation can give higher numerical performance with a min-imal impact on accuracy. We present the implementationof our numerical scheme on the GPU, discuss the accuracyof the approach, and benchmark how well it maps to theunderlying computational hardware.

Andr’e R. BrodtkorbSINTEF ICT, Department of Applied MathematicsAndre.Brodtkorb@sintef.no

Lateral Coupling of 1D-2D Shallow-Water Equa-tions

There are numerous situations in hydraulic engineering(dam breaks, flooding events...) that require numericalsimulation. Since large domains are often considered,yielding significant computational cost, it is still remain-ing a challenging domain.1D and 2D tools developed byElectricite De France, respectively called Mascaret andTelemac2D , are widely used to solve this kind of free sur-face flow problems. They are based on solution of the shal-low water equations. In this study, we aim at couplingthese two codes in order to benefit from their different as-sets in the same computation.. To this end, a lateral cou-pling technique without overlapping has been developed..This coupling based on transversal local Riemann solver isdescribed and validated on academic test cases.

Nicole GoutalEDF R&D & Saint-Venant Hydraulic Lab.nicole.goutal@edf.fr

martin parisotSaint-Venant Hydraulic Lab.martin.parisot@gmail.com

Fabrice ZaouiEDF R&Dfabrice.zaoui@edf.fr

Coupling 1-D and 2-D Shallow Water Equations forFlood Modelling

Rubar 3 and Rubar 20 developed by Irstea solved respec-tively 1-D and 2-D shallow water equations using similarfinite volume Godunov type second order schemes. Theircoupling is built on a calculation of the exchange termsusing the 2-D method. Two examples are shown: an ex-periment in which a pipe is connected with one street sim-ulating the calculation unit for urban flood and the annual

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flood in the Inner delta of the Niger River.

Andre PaquierIrsteaandre.paquier@irstea.fr

Bazin Pierre-HenriIrstea,UR HHLYpierre-henri.bazin@irstea.fr

Gilles BelaudEcole Nationale Superieure d’Agronomiebelaud@supagro.inra.fr

Computational Methods for Coupling 1D channelsin Complex Shallow Water Networks

We present two methods for coupling 1D channels in com-plex shallow water networks. In the first method, 1D chan-nels are connected through local 2D unstructured meshpatches. The second technique replaces the 2D patch bya single, specially chosen 2D element. Both methods workwell for all flow regimes, including bores, with CPU-timesavings of two orders of magnitude relative to a full 2Dtreatment.

Eleuterio F. ToroDepartment of Civil and Environmental EngineeringUniversity of Trento, Italytoro@ing.unitn.it

Francesca BellamoliLaboratory of Applied Mathematics, University of TrentoItalyfrancesca.bellamoli87@gmail.com

Lucas MuellerUniversity of Trento, Italylucas.mueller@gmail.com

En-Route Data Assimilation

Assimilation of data collected by Lagrangian or pseudo-Lagrangian instruments such as drifters, gliders, or floats,and in particular subsurface data, is of great interest, butdifficult because the subsurface paths are unknown. Ourrecent work introduces an observation operator which al-lows us to express these en-route observations as a func-tion of the state vector of the model at the measurementtime. We show the efficacy of this en-route data assimila-tion scheme.

Amit ApteTIFR Centre for Applicable MathematicsBangalore, Indiaapte@math.tifrbng.res.in

Elaine SpillerMarquette Universityelaine.spiller@marquette.edu

Christopher JonesUniversity of North Carolinackrtj@email.unc.edu

Towards Improvement of Climate Models UsingData Assimilation

The data assimilation problem is traditionally a state es-timation problem, combing observational data with a nu-merical model to create an improved estimate of the cur-rent state from which to make forecasts. We will look atthe inverse problem of using observational data coupledwith state-of-the-art data assimilation techniques to incre-mentally improve the forecast model. This will includeestimation of non-global parameters as well as stochasticparameterization of unseen dynamics.

Lewis MitchellThe University of VermontDepartment of Mathematics and StatisticsLewis.Mitchell@uvm.edu

Assimilation and Model Error for a 3D Ocean Pro-cess Model

A simple kinematic model of a wind-forced three dimen-sional ocean eddy can illuminate complex dynamics of thefluid flow. However, a kinematic model alone cannot hopeto perfectly describe reality or the data one may collect.As such we propose modeling the difference between thekinematic model and data as a random function which werefer to as a bias. Once the random function is fit, weuse the now bias-corrected kinematic model to explore theeddy dynamics.

Elaine SpillerMarquette Universityelaine.spiller@marquette.edu

DW HanUniversity of Massachusettesdongwon@student.umass.edu

Lawrence PrattWoods Hole Oceanographic Institutionlpratt@whoi.edu

Tamay OzgokmenUniversity of Miami/RSMAStozgokmen@rsmas.miami.edu

Pseudo-Orbit Gradient Descent for LagrangianData Assimilation

A nonlinear approach to data assimilation, known aspseudo-orbit gradient descent, is presented and illustratedin the context of assimilating Lagrangian tracer trajec-tories in two-dimensional flows of point-vortex systems.The approach centers on minimizing a cost function in se-quence space, initialized with the noisy observations. Thetracer advection equations augment the point vortex modelequations, allowing the observed tracer positions to up-date the state information about unobserved vortex posi-tions. Pseudo-orbit gradient descent has been successfullydemonstrated for the case of both full and partial observa-tions.

Emma SucklingCentre for Analysis of Time SeriesLondon School of Economics

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e.suckling@lse.ac.uk

Modeling Coupled Hydro-Mechanical Phenomenain the Near Field of a High-Level RadioactiveWaste Repository in Clay Formations

Clay/shale formations are being investigated as potentialhost rock for geological disposal of high-level radioactivewaste throughout the world. This presentation discussesadvanced computational methods for modeling the cou-pled hydro-mechanical processes occurring near repositorytunnels as a result of tunnel excavation, ventilation, wasteemplacement, and gas production. We also touch on howthese methods are being tested against in situ experimentaldata from underground research laboratories.

Jens T. BirkholzerLawrence Berkeley National Laboratory(LBNL)JTBirkholzer@lbl.gov

Daisuke Asahina, James Houseworth, Hui-Hai Liu, JonnyRutqvistLawrence Berkeley National Laboratory (LBNL)dasahina@lbl.gov, jehouseworth@lbl.gov, hhliu@lbl.gov,jrutqvist@lbl.gov

Can CCS Find Synergies with Geothermal Energyand Shale Gas Production?

Currently, the only realistic path forward for implementa-tion of large-scale Geological Carbon Storage is throughsynergistic activities that can provide positive economicdrivers for CO2 storage. Two such possibilities are CO2 in-jection as part of a geothermal production strategy, and in-jection of CO2 into depleted shale gas formations. Compar-ison of simulation approaches for these two systems withsimulation approaches for CO2 injection into deep salineaquifers highlights the challenges associated with these al-ternate strategies.

Michael A. CeliaPrinceton UniversityDept of Civil Engineeringcelia@princeton.edu

Coupled Thermal Models with Vertical Equilib-rium

Coupled thermal and fluid flow processes should be con-sidered when modeling CO2 injection and storage. Often,CO2 is injected at a different temperature than geothermalconditions, leading to significant density differences withinthe plume. This impact is particularly important for injec-tion sites near the critical point. We couple heat transferwithin the vertical equilibrium framework for fluid flow,which requires an upscaled representation of thermal pro-cesses. Simulations are performed for realistic geologicalstorage sites.

Sarah GasdaUniversity of North Carolina at Chapel Hillsarah.gasda@uni.no

Odd Andersen, Halvor Nilsen

Applied MathematicsSINTEF ICTodd.andersen@sintef.no, halvor.nilsen@sintef.no

Ivar AavatsmarkCIPR University of Bergenivar.aavatsmark@uni.no

Helge DahleDepartment of MathematicsUniversity of Bergenhelge.dahle@math.uib.no

Lifetime of Carbon Capture and Storage as a Cli-mate Change Mitigation Technology

In carbon capture and storage (CCS), CO2 is capturedat power plants and then injected underground into reser-voirs like deep saline aquifers for long-term storage. WhileCCS may be critical for the continued use of fossil fuelsin a carbon-constrained world, the deployment of CCS hasbeen hindered by uncertainty in geologic storage capacitiesand sustainable injection rates, which has contributed tothe absence of concerted government policy. Here, we clar-ify the potential of CCS to mitigate emissions in the UnitedStates by developing a storage-capacity supply curve that,unlike current large-scale capacity estimates, is derivedfrom the fluid mechanics of CO2 injection and trappingand incorporates injection-rate constraints. We show thatstorage supply is a dynamic quantity that grows with theduration of CCS, and we interpret the lifetime of CCS asthe time for which the storage supply curve exceeds thestorage demand curve from CO2 production. We showthat in the United States, if CO2 production from powergeneration continues to rise at recent rates, then CCS canstore enough CO2 to stabilize emissions at current lev-els for at least 100 years. This result suggests that thelarge-scale implementation of CCS is a geologically viableclimate-change mitigation option in the United States overthe next century.

Michael SzulczewskiMITCivil and Environmental Engineeringmszulcz@mit.edu

Christopher W. MacMinnMITMechanical Engineeringchristopher.macminn@yale.edu

Howard HerzogMITMIT Energy Initiativehjherzog@mit.edu

Ruben JuanesMITCivil and Environmental Engineeringjuanes@mit.edu

Multicore Aware Parallel Simulations of Co2 Geo-logical Storage

We enhance the parallel scalability of the general-purposeTough2-MP code to consider complex modeling. This talk

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will focus and the required adaptations of the assembly andthe solve phases considering the impact of the mapping ofthe processes on the physical cores. We will also commenton the extra-costs inferred by the memory hierarchy andthe bandwidth limitation. Some illustrative examples oflong-term fate of CO2 stored in reservoirs will also be de-tailed.

Fabrice DuprosBRGMORLEANS, FRANCEf.dupros@brgm.fr

Assessment of An Hpc Two-Phase Flow Solver inPorous Media for Realistic Cases

In this presentation we address the developments and per-formance of a two-phase flow solver for porous media. Thesoftware library implements the IMplicit Pressure/ExplicitSaturation (IMPES) algorithm. To address realistic cases,with millions of degrees of freedom and physical propertieswith strong variations, a parallel implementation is needed,along with a suitable choice of preconditioners. We presenthere some tools and techniques that can be used to achievegood performance on modern supercomputers.

Antonio CervoneMOX, Department of Mathematics Politecnico di Milano,Italyantonio.cervone@enea.it

Improving the Scalability of Reservoir Simulationon Multicore Architecture

Today, reservoir simulators have difficulties to fully har-ness the power of modern supercomputers: a simulationof several million of active cells barely scales over a fewhundred cores when large supercomputers count hundredsof thousands of cores. In this presentation, we discuss ourresearch to improve the scalability of a reservoir simula-tor by using a fine grain parallelization in an MPI/threadframework. We will focus on the linear solver part whichis the bottle-neck of such an approach.

Pascal HenonEP/DEV/GIS/SIMTotal Francepascal.henon@total.com

Corentin RossignonTOTALcorentin.rossignon@total.com

Compositional Two-Phase Flow with DisappearingNonwetting Phase - Modeling and Numerical Sim-

ulation of CO2 Sequestration

Carbon Capture and storage is simulated with a two-phasetwo-component flow model employing a special set of pri-mary variables (capillary pressure / phase pressure) to dealwith the (dis-)appearance of the nonwetting phase. Theimplementation is based on DUNE PDELab. Numericalresults of massive parallel simulations for test cases withmillions of unknowns on hundreds of cores on the supercomputer HERMIT (Cray X6) are presented and discussed.

Rebecca NeumannInterdisziplinares Zentrum fur WissenschaftlichesRechnen (IUniversitat Heidelberg, Germanyrebecca.neumann@iwr.uni-heidelberg.de

Discontinuous Galerkin Multiscale Methods for El-liptic Problems

A discontinuous Galerkin multiscale method for flow inporous media is proposed. Convergence results are pre-sented both for diffusion and convection dominated prob-lems, with heterogeneous data without any assumption onscale separation or periodicity. The multiscale method usesa corrected basis that is computed on patches/subdomains.Linear convergence in energy norm is obtained indepen-dently of the data. Numerical experiments confirms thetheoretical rates of convergence.

Daniel ElfversonUniversity of Uppsala (Sweden), Div. ScientificComputingDept. Information Technologydaniel.elfverson@it.uu.se

Axel MalqvistUppsala Universityaxel.malqvist@it.uu.se

Daniel PeterseimHumboldt-Universitaet zu BerlinInstitut fur Mathematikpeterseim@math.hu-berlin.de

Discontinuous Galerkin Multiscale Methods forAdvection-Diffusion Problems with Highly Hetero-geneous Data

In this talk, we introduce a discontinuous Galerkin het-erogeneous multiscale method (DG-HMM) for advection-diffusion problems with highly heterogeneous data. Wediscuss the stability of the method for both advection anddiffusion dominated problems and for general data. Fur-ther, we present fully discrete a priori error estimates forlocally periodic data. Moreover, we show that under scale

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separation assumption (e.g., local periodicity) the compu-tational work is independent of the smallest scale in themedium.

Assyr AbdulleEPFL - Ecole Polytechnique Federale de Lausanneassyr.abdulle@epfl.ch

Martin Huber

Ecole Polytechnique Federale de Lausanne (Switzerland)Mathematics Institute of Computational Science &Engineeringmartin.huber@epfl.ch

On Oversampling for the Multiscale Finite ElementMethod

In this talk, we review several oversampling strategies asperformed in the Multiscale Finite Element Method (Ms-FEM). Common to those approaches is that the oversam-pling is typically performed in the full fine scale space re-stricted to a patch. We suggest, by contrast, to performlocal computations with additional constraints. The newsetting gives rise to a general fully discrete error analy-sis for the proposed multiscale method with oversamplingwithout suffering from resonance effects.

Patrick HenningUniversity of Munster,Institut fur Numerische und Angewandte Mathematikpatrick.henning@uni-muenster.de

Daniel PeterseimHumboldt-Universitaet zu BerlinInstitut fur Mathematikpeterseim@math.hu-berlin.de

Probabilistic Models of Earthquake Slip forTsunami Hazard Assessment

Probabilistic Tsunami Hazard Assessment (PTHA) for acommunity requires sampling the earthquake parameterspace of possible seismic events that may cause tsunamis.The distribution of slip on a given fault geometry cangreatly affect the resulting inundation, particularly in thenearfield. Recent work will be presented on the use ofKarhunen-Loeve expansions to represent slip on the Cas-cadia Subduction Zone, and use of these models togetherwith GeoClaw for PTHA on the coast of California and thePacific Northwest.

Randall J. LeVequeApplied MathematicsUniversity of Washington (Seattle)rjl@uw.edu; rjl@amath.washington.edu; rjl@washingt

Knut Waagan, Frank I. GonzalezUniversity of Washingtonkwaagan@gmail.com, figonzal@u.washington.edu

Guang LinPacific Northwest National Laboratoryguang.lin@pnnl.gov

Effect of Heterogeneous Earthquake Slip onTsunami Run-Up Uncertainty

We first review investigations of tsunami propagation dueto heterogeneous slip, with emphasis on uncertainty andpredictability. A systematic study of plane wave propaga-tion and uncertainty propagation due to heterogeneous slipfrom earthquake slip scaling laws all the way to run-up isthen presented. Non-hydrostatic hydrodynamic effects aregiven particular attention. Finally, the effect of heteroge-neous slip from real cases such as the 2011 Tohoku tsunamiis briefly discussed.

Finn LovholtNorwegian Geotechnical Institute (NGI)finn.lovholt@ngi.no

Modelling Tsunamis and Problems Constrainingthe Slip in Mega-Thrust Earthquakes

Mega-thrust earthquakes and tsunamis cause untold de-struction. In this talk a new finite volume unstructuredgrid tsunami model is presented. The model is a finitevolume analogue of the Pnc

1 - P1 finite element, in whichmass conservation is guaranteed not only in a global sense,but within each cell. The model conserves momentum, andaccurately handles flooding and drying problems. Resultsfrom the Indian Ocean and Japanese Tsunami comparewell with flooding and run-up data.

Julie PietrzakFaculty of Civil Engineering and GeosciencesDelft University of Technologyj.d.pietrzak@tudelft.nl

H Cui, G.S. StellingDelft University of Technologyh.cui@tudelft.nl, g.s.stelling@tudelft.nl

Modeling Dynamic Rupture with Implications forAn Alaskan-Aleutian Megathrust Earthquake andResulting Tsunami

We investigate the effects of rate-strengthening-like fric-tion (e.g., Dieterich, 1992) and heterogeneous fault pre-stress on rupture propagation, slip, free surface deforma-tion, and the resultant tsunami in time (Shuto, 1991; Sa-take, 2002). Using time-weakening friction as a proxy forrate-strengthening friction, and given fault data along theAlaska-Aleutian megathrust assembled from the ScienceApplication for Risk Reduction team (SAFRR), we areable to dynamically model a Mw9 earthquake and resul-tant tsunami on a similar megathrust.

Kenny J. RyanDepartment of Earth SciencesUniversity of California, Riverside0k.ryan0@gmail.com

David D. OglesbyDepartment of Earth Sciences, Univ. of CA, Riverside900 University Ave. Riverside, CA 92521david.oglesby@ucr.edu

Eric L. GeistUS Geological Survey

118 GS13 Abstracts

egeist@usgs.gov

A Multilevel Domain Decomposition Algorithm forFluid-structure Interaction in Porous Media

In this talk we consider multilevel domain decompositionalgorithms for the numerical solution of fluid structure in-teraction problems for flows in porous media. From thephysical point of view, the use of this class of algorithmsis motivated by the need to solve fluid filtration problemsin porous media which are characterized by a high hetero-geneity in terms of length scale, as it occurs for instancein the case of fractured porous media with complicatedgeometries. From the numerical point of view, multileveldomain decomposition algorithms are defined with the pur-pose of combining the advantageous features of both geo-metric multigrid and domain decomposition methods, suchas optimal computational complexity and parallelizable im-plementation. We investigate the performances of the al-gorithm in terms of accuracy and computational efficiencyby considering the results of some numerical tests for fluid-structure problems naturally arising in the study of porousmedia fluid flows.

Giorgio BorniaDept. of Mathematics and Statistics Texas TechUniversitygiorgio.bornia@ttu.edu

Sandro ManservisiLaboratory of MontecuccolinoDIN, University of Bolognasandro.manservisi@unibo.it

Realistic Scale Simulations of Sedimentary Basins

A parallel implementation for the development and evolu-tion of sedimentary basins is proposed. Rocks are modeledas highly viscous fluids in creeping flow regime. When deal-ing with realistic scales, the number of degrees of freedombecomes huge, and the solution of the discretized problembecomes challenging, especially in the presence of high vari-ations in the physical parameters. In particular, precondi-tioners that scale well with respect to parallel processes,viscosity ratios and dofs are analyzed.

Antonio CervoneMOX, Department of Mathematics Politecnico di Milano,Italyantonio.cervone@enea.it

Nur A. FadelPolitecnico di Milano - MOX - Dipartimento diMatematicanur.fadel@mail.polimi.it

Modeling Mulitscale and Multiphase Flow inPorous Media

We consider multiphase flow, e.g. water and air, in porous

media, using an upscaling approach to recently derivedphase field models. To this aim, we combine rational ther-modynamics, i.e. the assumption of maximum rate of en-tropy production by Rajagopal and Srinivasa, with for-mal asymptotic expansion. The result will be a family oftwoscale models for several types of microscopic regimes.

Martin HeidaUniversitat Heidelbergmartin.heida@iwr.uni-heidelberg.de

Water Transport in Partially-molten Ice - A Multi-phase Theory Approach

We present a two-phase model for thermo-mechanical evo-lution of partially molten ice and gravity-driven water ex-traction. We perform scale analysis and associated modelreduction in a physical setting relevant for conditions inthe ice layers of moons of outer planets in the solar sys-tem (Europa, Enceladus). We revisit the traditional zerocompaction length approximation, obtained by omission ofthe coupling effects between melt flow and ice deformation.We numerically investigate the relation between the shock-like solutions of the zero compaction length model and thewave-train solutions of the full model and examine the ef-fects of the zero compaction length approximation on thecharacter of the water transport.

Ondrej Soucek SoucekCharles Universitysoucek@karel.troja.mff.cuni.cz

Using the Gibbs-Helmholtz Constrained Eos inReservoir Simulation

This talk will provide an overview of a general frameworkfor multi-component, multi-phase equilibrium flash calcu-lations, which uses the multi-scale Gibbs Helmholtz Con-strained (GHC) equation, and discuss the reliability andefficiency of the flash algorithm, how they are measured,and their relationship to reservoir simulator performance.The multi-scale GHC equation flash algorithm, GFLASH,has been coupled to the Stanford University reservoir sim-ulator, AD-GPRS. Reservoir simulation examples and geo-metric illustrations are presented to elucidate key concepts.

Angelo LuciaDepartment of Chemical EngineeringUniversity of Rhode Islandlucia@egr.uri.edu

Calculation of Phase Equilibrium: Status and Per-spectives

The talk presents an overview of selected computationalmethods for calculation of phase equilibrium. Topics areequilibrium calculations of relevance for compositional sim-ulation with the classical cubic equation of state. In ad-dition the computational aspects of implementing complexequations of state like SAFT are discussed. For such equa-

GS13 Abstracts 119

tions, formulation in terms of volume rather than pressuremay be preferable.

Michael L. MichelsenTechnical University of Denmarkmlm@kt.dtu.dk

Gibbs Free Energy Minimization for Reactive Flowin Porous Media

The modeling of CO2 injection for enhanced oil recoveryin carbonate reservoirs entails complex interplay of flow,geochemical reactions and hydrocarbon phase behavior. Anew framework for compositional simulation is introducedthat integrates reactions and phase behavior using localequilibrium assumption. The equilibrium composition issolution to the constrained nonlinear optimization of theGibbs free energy function for the system. Two applica-tions are discussed – acid gas solubility and hydrocarbonphase changes in presence of reactions.

Ashwin Venkatraman, Larry LakeThe University of Texas at Austinashwin.venkatraman@utexas.edu, larry.lake@utexas.edu

Russell JohnsPenn State Universityrjohns@psu.edu

Multi-Linear Representation of Phase Behavior forLarge Scale Gas Injection Simulation

We describe an AdaptiveCompositional Space Parametrization (ACSP) method forcompositional flow simulation. The method is based oncasting the nonlinear governing equations in terms of thetie-simplex. The tie-simplex space is directly discretizedusing a limited number of tie-simplexes. The coefficients inthe governing system of equations, including the composi-tion, density, and mobility of the phases, are computed us-ing multilinear interpolation in the discretized space. TheACSP completely replaces all the standard EOS computa-tions

Rustem ZaydullinStanford Universityrustemz@stanford.edu

Block-Structured Adaptive Mesh Refinement inthe Bisicles Ice Sheet Model

The BISICLES ice sheet model employs a block-structuredmesh of rectangular cells to obtain high resolution at thegrounding line. In some ways that is restrictive comparedto (say) an unstructured mesh of triangles, but it has three

points in its favor. First, it is straightforward to use newmeshes as a simulation progresses. Second, it is naturalto construct a geometric multigrid solver for the stress-balance equations. Thirdly, domain decomposition is easy.

Stephen CornfordUniversity of Bristols.l.cornford@bristol.ac.uk

Daniel MartinLawrence Berkeley National Laboratorydfmartin@lbl.gov

Grounding Line Migration in a Full-Stokes Model:from Processes to Applications

We examine here the possibility of modeling Antarcticoutlet glaciers using the full-Stokes finite-element modelElmer/Ice. Process studies of the grounding line dynamicson synthetic regular bedrocks are first discussed and com-pared with analytical results. Further simulations showingthe evolution of actual systems are presented and comparedwith obserbations.

Gael DurandLaboratoire de Glaciologie et de Geophysiquede l’Environnemt, Grenoble, Francedurand@lgge.obs.ujf-grenoble.fr

Olivier Gagliardini, Lionel FavierLGGEgagliar@ujf-grenoble.fr, lionel.favier@ujf-grenoble.fr

Thomas ZwingerCSCzwinger@csc.fi

Anne-Sophie Drouet, Jean Krug, Fabien Gillet-ChauletLGGEdrouet@ujf-grenoble.fr, jean.krug@ujf-grenoble.fr, gillet-chaulet@lgge.obs.ujf-grenoble.fr

Mesh-adaptive Approaches to Numerical Ground-ing Line Migration

Central to the evolution of marine ice sheets that could po-tentially make large contributions to sea level rise in com-ing centuries is the evolution of grounding lines, a processdifficult to represent numerically, largely due to issues ofresolution. I will show numerical results of several mesh-adaptive approaches that attempt to deal with these issues.I will discuss the strengths of weaknesses of each approach,and compare with an existing quasi-analytical approach.

Daniel GoldbergDepartment of Earth, Atmospheric, and PlanetarySciencesMassachusetts Institute of Technology, Cambridge, USAdngoldberg@gmail.com

Review of Adaptive Methods for Marine Ice SheetModels

Adaptive mesh refinement methods are required to account

120 GS13 Abstracts

for the sharp changes of the dynamical regime of ice in thetransition zones between ice sheets and ice shelves. Theempirical criterion, which consists of strongly refining closeto the grounding line, is easy to implement but not opti-mal. In contrast, a new family of methods based on errorestimates has appeared in recent years. This talk aims togive a comparative overview of such methods.

Guillaume JouvetFreie Universitat BerlinInstitut fur Mathematikguillaume.jouvet@fu-berlin.de

One-Dimensional Finite-Volume Modelling of theFlow and Morphological Processes During the 1996Lake Ha!Ha! Dyke Break Event

The Lake Ha!Ha event is chosen as an example of extremeflow to highlight two key issues in numerical simulationsof real events: the discretisation of topographical sourceterms in very irregular and evolving cross-sections, andthe representation of morphological processes when ero-sion affects the river banks as well as the river bed. Afinite-volume modelling framework is used to conduct theanalysis first from a pure hydrodynamical point of view,and secondly by including morphological processes.

Sandra Soares-FrazaoInstitute of Mechanics, Materials and Civil EngineeringEcole Polytechnique de Louvainsandra.soares-frazao@uclouvain.be

Fabian FranziniEcole Polytechnique de Louvainfabian.franzini@student.uclouvain.be

Olivier Carlier, Yves ZechInstitute of Mechanics, Materials and Civil EngineeringEcole Polytechnique de Louvainolivier.carlier@uclouvain.be, yves.zech@uclouvain.be

2D Depth Integrated Modeling of Morphodynami-cal Processes: A New Algorithm for UnstructuredGrids

In recent years many complex multi-phase or multi-layermodels were proposed for modeling water and sedimentflows in unsteady conditions. Moreover representation ofcomplex geometries can be achieved using a unstructuredmesh. In the present paper an ad-hoc algorithm for un-structured triangular cells is proposed. It is demonstratedthat the algorithm is globally mass-preserving. Effective-ness of the proposed approach is demonstrated by the nu-merical integration of the morphodynamic model proposedby Greco et Al. (2012).

Angelo LeopardiDIPARTIMENTO DI INGEGNERIA CIVILE EMECCANICAUniversita di Cassino, Italya.leopardi@unicas.it

Massimo GrecoUniversity of Naplesgrecom@unina.it

Stefania Evangelista

University of Cassino and Southern Lazios.evangelista@unicas.it

Michele Iervolino, Andrea VaccaSecond University of Naplesmichele.iervolino@unina2.it, vacca@unina.it

Local Adaptive Mesh Refinement on the GPU

We present the implementation of adaptive mesh refine-ment (AMR) for shallow water simulation on the GPU.AMR significantly increases accuracy, with little impacton computational cost compared to increasing grid resolu-tion for the entire domain. Mapping the AMR algorithmto the GPU, however, is non-trivial. Our implementationtargets the second-order accurate Kurganov-Petrova cen-tral scheme. We present implementation details, difficul-ties, key insights, and performance benchmarks.

Martin L. StraCentre of Mathematics for ApplicationsUniversity of Oslomartinsa@cma.uio.no

A GPU Implementation of High-Order PVM FiniteVolume Schemes for Shallow Flows on TriangularMeshes

In this work we present a CUDA implementation of thehigh-order WENO reconstruction operator proposed by M.Dumbser and M. Kaser for triangular meshes. We usethis reconstruction operator in combination with the PVM-IFCP sheme in order to simulate one an two-layer shallowwater flows achieving second and third order accuracy. Fi-nally, we perform an analysis of the obtained precision andefficiency with respect to CUDA implementations of thefirst order PVM-IFCP scheme for one and two-layer shal-low water systems.

Marc de la Asuncion, Jose M. MantasUniversity of Granadamarc@correo.ugr.es, jmmantas@ugr.es

Manuel J. CastroUniversity of Malagacastro@anamat.cie.uma.es

Targeting Observations and Parameter EstimationTechniques Within Ensemble Data Assimilation

We explore novel data assimilation techniques for twomodel problems of potential meteorological interest. Usingthe local ensemble transform Kalman Filter (LETKF), ourmain result demonstrates LETKF with targeted observa-tions based on largest ensemble variance is skillful by out-performing LETKF with randomly located observations.We implement the parameter estimation method SPEEKto further improve state estimation. We also determinethe effect that number of observations, ensemble size, andlocalization radius have on state estimation.

Thomas BellskyArizona State Universitybellskyt@asu.edu

GS13 Abstracts 121

Eric J. KostelichArizona State UniversitySchool of Mathematical & Statistical Scienceskostelich@asu.edu

Alex Mahalovdepartement of mathematics,Arizona State Universitymahalov@asu.edu

The Onset of Desertification: the Dynamics of Veg-etation Patterns under Slowly Varying Conditions

In this talk we introduce a conceptual model for vegeta-tion patterns in semi-arid ecosystems on sloped terrains.We consider the onset of pattern formation through aTuring/Turing-Hopf bifurcation by varying the parameter(A) that measures yearly rainfall. We numerically con-struct Busse balloons to follow the family of stable spa-tially periodic (vegetation) patterns into the realistic areaof localized vegetation patterns. Next, we assume that Ais a slowly decreasing function and study the trajectoryof the patterns through the Busse balloon. We find thatthe vegetation patterns undergo ‘mini-catastrophes’ as thetrajectory approaches the boundary of the Busse balloonbefore they reach the final catastrophe of desertification.

Arjen DoelmanMathematisch Instituutdoelman@math.leidenuniv.nl

Pseudo-Orbit Data Assimilation for AtmosphericGcms

Data assimilation for nonlinear models such as weatherforecasting models is a challenging task. A promising al-ternative approach is proposed to produce more consistentestimates of the model state, and to estimate the (statedependent) model error simultaneously, using the Pseudo-orbit Data Assimilation method with a stopping criteria.This method is shown to be more efficient and more co-herent than the variational method and outperform theEnsemble Kalman Filter in nowcast on large scale models.

Hailiang DuCentre for Analysis of Time SeriesLondon School of Economicsh.l.du@lse.ac.uk

Automatic Identification of Oceanic and Atmo-spheric Coherent Structures As Minimal Flux Re-gions Using Transfer Operators

Optimally coherent sets are the most efficient transportersof geophysical flow mass (eg. water mass or air mass). Wedescribe a recent numerical method that uses Lagrangianinformation to detect and track optimally coherent sets intime-dependent geophysical flows. We illustrate the newapproach by tracking Agulhas rings, and accurately deter-mining the locations of the Antarctic polar vortex. Themethod works naturally in two- and three-dimensions, andcan handle both advective and advective/diffusive dynam-ics.

Gary Froyland

University of New South Walesg.froyland@unsw.edu.au

Christian HorenkampChair of Applied MathematicsUniversity of Paderbornchristian.horenkamp@math.upb.de

Adam MonahanSchool of Earth and Ocean SciencesUniversity of Victoriamonahana@uvic.ca

Vincent RossiUNSW, Australia,v.rossi@unsw.edu.au

Alex Sen GuptaUNSW, Australiaa.sengupta@unsw.edu.au

Erik van SebilleUniversity of New South Walese.vansebille@unsw.edu.au

Experimental Investigation of Shale Gas Produc-tion Impairment Due to Spontaneous Imbibition ofFracturing Fluid Following Wellbore Stimulation.

A series of laboratory experiments were conducted tomimic spontaneous imbibition of water-based fracturingfluid into fractured shale formations and investigate its im-pact on gas production impairment. The imbibing frontwas monitored using X-ray computed tomography, whichallowed us to map saturation at controlled time intervals.Results are compared against similar experiments in tightsand and Berea sandstone samples in terms of regainedpermeability and evolution of saturation profiles.

Zuleima T. Karpyn, Luis AyalaEnergy and Mineral EngineeringThe Pennsylvania State Universityzkarpyn@psu.edu, ayala@psu.edu

Competitive Usage of Sub-Surface Systems: HowCan Modeling Help to Quantifiy Potential Impactsand Risks?

Global climate change, shortage of resources and the grow-ing usage of renewable energy sources has lead to a growingdemand for the utilization of subsurface systems. Amongthese competing uses are Carbon Capture and Storage(CCS), geothermal energy, nuclear waste disposal, ”renew-able” methane or hydrogen storage as well as the ongoingproduction of fossil resources like oil, gas and coal. Addi-tionally, these technologies may also create conflicts withessential public interests such as water supply. For ex-ample, the injection of CO2 into the subsurface causes anincrease in pressure reaching far beyond the actual radiusof influence of the CO2 plume, potentially leading to largeamounts of displaced salt water. In order to be able toasses the large scale impacts of different technologies it isnecessary not only to consider the reservoir itself but alsothe regional hydrogeology. This is especially important forthe vertical migration of displaced formation fluids or con-taminants. Structures such as fault zones or salt domes are

122 GS13 Abstracts

considered as potential pathways for displaced fluids intoshallow systems and their influence has to be taken intoaccount.

Holger ClassUniversitaet StuttgartScientistholger.class@iws.uni-stuttgart.de

Alexander KissingerUniversitaet Stuttgartalexander.kissinger@iws.uni-stuttgart.de

Simulation of Coupled Flow and Reactive Trans-port in Porous Media by MFEM with Applicationto Concrete Carbonation

We discuss a prototypical reaction-diffusion-flow scenarioin saturated/unsaturated porous media. The special fea-tures of our scenario are: the reaction produces water andtherefore the flow and transport are coupled in both direc-tions and moreover, the reaction may alter the microstruc-ture. This means we have a variable porosity in our model.For the spatial discretization we propose a mass conser-vative scheme based on the mixed finite element method.The scheme is semi-implicit in time. Error estimates areobtained for some particular cases. We apply our finiteelement methodology for the case of concrete carbonation– one of the most important physico-chemical processesaffecting the durability of concrete.

Florin A. Radu, Florin A. RaduInstitute of MathematicsUniversity of Bergenflorin.radu@math.uib.no, florin.radu@math.uib.no

Adrian MunteanDepartment of Mathematics and Computer ScienceTU Eindhovena.muntean@tue.nl

Iuliu Sorin PopDept of Mathematics and Computer SciencesTU EindhovenI.Pop@tue.nl

Gampack (gpu Algebraic Multigrid Package)

Algebraic multigrid (AMG) has become the preconditionerof choice for solving the pressure subblock of multiphaseflow matrices. The serial and irregular nature of traditionalAMG algorithms has made accelerating them on massivelyparallel processors difficult. We discuss the approacheswe have used to successfully accelerate AMG on multi-ple GPUs by employing algorithms with sufficient fine-grained parallelism. We then compare the performance ofour GAMPACK solver with CPU-based AMG solvers formatrices arising from reservoir simulation.

Vincent Natoli, Kenneth EslerStone Ridge Technologyvnatoli@stoneridgetechnology.com,kesler@stoneridgetechnology.com

Arcfvdsl, a Dsl in C++ to Develop Diffusive Prob-

lems in Geoscience for New Hybrid Architecture

Industrial simulation software have to manage: (i) thecomplexity of the underlying physical models, (ii) thecomplexity of numerical methods used to solve the PDEsystems, and finally (iii) the complexity of the low levelcomputer science services required to have efficient soft-ware on modern hardware. Nowadays, some frameworksoffer a number of advanced tools to deal with the com-plexity related to parallelism in a transparent way. How-ever, high level complexity related to discretization meth-ods and physical models lack of tools to help physiciststo develop complex applications. Generative programmingand domain-specific languages (DSL) are key technologiesallowing to write code with a high level expressive languageand take advantage of the efficiency of generated code forlow level services. In our paper, we present a C++ DomainSpecific Embeded Language (DSEL) to implement multi-scale methods for elliptic problems in porous media with ahigh level of abstraction allowing to separate the low levellayer necessary to have performance on new hybrid het-erogeneous mutiprocessors architecture with data-parallelaccelerators. We focus on the capability of the languageto design complex multi-scale methods and we present theabstract object oriented runtime system model allowing toadress heterogeneous architecture. We present some per-formance results on various hybrid platforms.

Jean Marc GratienIFPjean-marc.gratien@ifp.fr

Scalability of a Multi-Phase Code for PerformanceAssessment of a Radioactive Waste Disposal inPorous Media

The French National Radioactive Waste ManagementAgency (Andra) runs numerical simulations to assess per-formance of radioactive waste disposal in geological me-dia. Parallel mpi based code TOUGH2-MP has beenused for years to perform multi-phase simulations on thistopic.According to grid of millions cells and long time sim-ulated, scalability of TOUGH2-MP has been studied onLinux clusters (Intel and AMD) up to 2048 cores for vari-ous physical situations and results are presented here.

Bernard VialayAndraFrancebernard.vialay@andra.fr

Multi-GPU Parallelization of Nested FactorizationLinear Solver

We describe a massively parallel Nested Factorization (NF)linear solver. The key features are: 1) a special ordering ofthe matrix elements that maximizes coalesced memory ac-cess, 2) application of twisted factorization, which doublesconcurrent threads at no additional cost, and 3) extensionto multiple GPUs by overlapping memory transfer betweenGPUs with solution of the interior regions. The 6-GPU so-lution of a 26.9M-cell model is more than five times fasterthan the single-GPU solution.

Yifan ZhouStanford University(Now with Chevron Energy Technology Company)yifanz@stanford.edu

GS13 Abstracts 123

The Localized Reduced Basis Multiscale Method

We present the Localized Reduced Basis Multiscale(LRBMS) method for parameter dependent heterogeneouselliptic multiscale problems [F. Albrecht, B. Haasdonk,S. Kaulmann, and M. Ohlberger. The Localized Re-duced Basis Multiscale Method. In A. Handlovicovaand Z. Minarechova and D. Sevcovic (editor(s)): AL-GORITMY 2012 - Proceedings of contributed papers andposters (2012), 393–403]. This method brings togetherideas from both Reduced Basis methods to efficiently solveparametrized problems and from multiscale methods inorder to deal with complex heterogeneities and large do-mains. We present recent developments of the method andapplications in the two-phase flow context.

Felix AlbrechtUniversity of Munster (Germany)Institute for Computational und Applied Mathematicsfelix.albrecht@uni-muenster.de

Bernard Haasdonk, Sven KaulmannUniversity of Stuttgarthaasdonk@mathematik.uni-stuttgart.de,sven.kaulmann@mathematik.uni-stuttgart.de

Mario OhlbergerUniversitat MunsterInstitut fur Numerische und Angewandte Mathematikmario.ohlberger@uni-muenster.de

Analysis of a Control Volume Hmm for Multi-Physics Problems in Porous Media

We discuss conservative methods based on the heteroge-neous multiscale methodology. The key ingredients are lo-cally conservative control volume methods on the coarsescale, coupled with local solvers for the fine scale prob-lems, thus providing proper effective relationships amongcoarse scale parameters. We place particular emphasis onproper handling of coarse-scale heterogeneities.

Sergey AlyaevUniversity of BergenDepartment of Mathematicssergey.alyaev@math.uib.no

Eirik KeilegavlenUniversity of BergenEirik.Keilegavlen@uib.no

Coupled Local-Global Model Reduction for Com-pressible Flows in Highly Heterogeneous Porous

The governing equations for porous media problems con-sist of coupled processes that can vary over multiple scales.Because of disparity of scales, the direct numerical simula-tions of these processes are prohibitively expensive. Thispresents the need to develop simplified models to signifi-cantly reduce the number of degrees of freedom while ne-glecting irrelevant details of the involved physics. In thiswork, we apply dynamic mode decomposition (DMD) andproper orthogonal decomposition (POD) on compressibleflows in highly heterogeneous porous media to extract thedominant coherent structures and derive a reduced-ordermodel. Different permeability fields are considered to in-vestigate the capability of these techniques to capture themain flow characteristics and reconstruct the flow fieldwithin a certain accuracy. In most of the cases, DMD-based approach showed a better predictive capability.

Mehdi GhommemKing Abdullah University of Science and Technology(KAUST)Division of Physical Sciences & Engineering (PSE)mehdig@vt.edu

Yalchin Efendiev, Michael PreshoDepartment of Mathematics & ISCTexas A&M Universityyalchinrefendiev@gmail.com, mpresho@math.tamu.edu

Victor M. CaloKing Abdullah University of Science and Technology(KAUST)Division of Physical Sciences & Engineering (PSE)victor.calo@kaust.edu.sa

Computation of Eigenvalues by Numerical Upscal-ing

We present a numerical upscaling technique for computingeigenvalues of selfadjoint elliptic operators with multiscalecoefficients. We compute a low-dimensional generalized fi-nite element space that preserves small eigenvalues in a su-perconvergent way. The approximate eigenpairs are thenobtained by solving the corresponding low-dimensional al-gebraic eigenvalue problem. The rigorous error bounds areprovided.

Axel MalqvistUppsala Universityaxel.malqvist@it.uu.se

Daniel PeterseimDepartment of MathematicsHumboldt-Universitat zu Berlinpeterseim@math.hu-berlin

Discontinuous Galerkin Unsteady Discrete AdjointMethod for Real-Time Efficient Tsunami Simula-tions

An unsteady discrete adjoint implementation for a discon-tinuous Galerkin model solving the shallow water equa-tions on the sphere is presented. Its use for tsunami sim-ulations is introduced to reconstruct the initial conditionautomatically from buoy measurements. Based on this fea-ture, a real-time tsunami model is developed, using several

124 GS13 Abstracts

numerical tools such as a high-order discretization, hp-refinement, parallel dynamic load balancing and adjoint-based data assimilation. The model is able to reconstructthe tsunami source and accurately forecast its far-fieldpropagation in a computational time 20 times faster thanthe physical propagation time. The work presented consti-tutes a step towards an efficient nonlinear tsunami warningmodel. Additional features could be added for more com-plete realistic forecasts.

Sebastien BlaiseInstitute of Mechanics, Materials and Civil EngineeringUniversite catholique de Louvainsebastien.blaise@uclouvain.be

Amik St-CyrComputation and Modeling,Shell International E&P, Inc.amik.st-cyr@shell.com

Dimitri MavriplisDepartment of Mechanical EngineeringUniversity of Wyomingmavripl@uwyo.edu

Brian LockwoodUniversity of Wyomingblockwoo@uwyo.edu

Quadrilateral-Based Discontinuous Galerkin Meth-ods with Adaptive Mesh Refinement for theOceanic Shallow Water Equations

In recent years, we have been working on a triangle-baseddiscontinuous Galerkin shallow water model for simulat-ing tsunamis. This model, DGCOM, is a semi-automatedsystem that allows a user to build a grid along any coastalregion and then run the problem. However, DGCOM neverincluded any type of adaptive mesh refinement (AMR). Re-cently, we have developed a quadrilateral-based discontin-uous Galerkin AMR code for various applications includ-ing the 1) nonhydrostatic atmosphere and 2) shallow wateron the sphere, and more recently 3) shallow water on theplane. In this talk I will describe this new model which wecall NUMACOM and will show some benchmark test casesand discuss the addition of inundation algorithms for thishigh-order quadrilateral-based DG AMR model.

Francis X. Giraldo, Michal A. KoperaNaval Postgraduate Schoolfxgirald@nps.edu, makopera@nps.edu

Shivasubramania GopalakrishnanIndian Institute of Technologysgopalak@iitb.ac.in

Modeling of Tsunami Generation by An Underwa-ter Landslide

A high-resolution model solving for dynamics of a stack ofshallow layers in curvilinear co-ordinates has been devel-oped for simulating landslides that can serve as source oftsunami waves. The model relies on the reduced-gravityapproximation and solves nonlinear, hydrostatic or non-hydrostatic equations for horizontally inhomogeneous, vis-cous fluid layers on an f-plane. The dynamical equations

are discretized by the finite-difference method and inte-grated on a rectangular grid, which is the map of the curvi-linear grid generated by the elliptic method. Verificationand validation of numerical model is performed against thelaboratory experiment by Heller (2007) and megatsunamiLituya Bay event.

Natalja RakowskyAlfred-Wegener-Institute for Polar and Marine ResearchAm Handelshafen 12, 27570 Bremerhaven, Germanynatalja.rakowsky@awi.de

Alexey AndrosovAWIalexey.androsov@awi.de

Sven HarigAlfred-Wegener-Institute for Polar and Marine Researchsven.harig@awi.de

Implementation of Triangular Galerkin TypeAdaptive Tsunami Propagation and InundationSchemes

A tsunami simulation framework is presented, which isbased on adaptive triangular meshes with finite elementGalerkin type discretizations. This approach allows forhigh local resolution and geometric accuracy, while main-taining the opportunity to simulate large spatial domains.Within this framework, different discretizations are imple-mented and compared concerning efficiency and accuracy.Furthermore, the whole evolution of a tsunami event is in-vestigated, from the excitation to the inundation event atthe coast.

Stefan VaterUniversity of Hamburg, KlimaCampusstefan.vater@zmaw.de

The Multidimensional Muskat Inial BoundaryValue Problem

We consider the Muskat Problem for a generalized formu-lation to Darcy’s law equation (Darcy-Brinkman’s law).We follow our original idea established in previous work,which is to perturb the Darcy law equation with a positive(small as needed) viscosity term. The mathematical modelis formulated as

∂tρ+ v · ∇x ρ = 0, ∂tν + v · ∇x ν = 0,

h(t,x, μ) v − divx

(μ Dv

)= −∇xp+ ρf , divxv = 0,

where v is the velocity field, ρ−the density, ν−the effectiveviscosity and μ = ρν−the dynamic viscosity. The general-ized Muskat Problem is posed in a bounded domain of RN

for two-phase flow (oil-water), that seems more realisticfrom the physical point of view. We show the solvabilityof the initial boundary value problem for the system. Thisis primarily joint work with Wladimir Neves (Institute ofMathematics, Federal University of Rio de Janeiro).

Nikolai ChemetovCenter of Mathematics, Universidade de Lisboa

GS13 Abstracts 125

chemetov@ptmat.fc.ul.pt

Blow-up and Vanishing Properties for a Class ofDoubly Degenerate Parabolic Equations with Vari-able Nonlinearity

Anisotropy and variable nonlinearity lead to certain prop-erties intrinsic for the solutions of doubly degenerateparabolic equations of this type. We discuss the influenceof anisotropy on the blow-up and vanishing of solutionsand show that for equations with variable nonlinearity theeffects of finite time vanishing and blow-up may happeneven if the equation becomes linear at time infinity.

Sergey ShmarevUniversidad de Oviedoshmarev@uniovi.es

Regularity of Solutions to Weighted Equations ofPorous Medium Type

We establish the Harnack inequality and continuity fornonnegative solutions of nonlinear parabolic equations ofporous medium type in the presence of weight. This workincorporates the recent improvements brought to regularitytheory by Di Benedetto, Gianazza and Vespri and greatlysimplifies the proofs obtained by Ivanov in 80s.

Mikhail D. SurnachevInsitute of applied mathematics,Russion Academy of Science,peitsche@yandex.ru

Geometric PDE Models for Secondary Structure inProteins

This report represents a small part of an extensive researchproject regarding elastic membranes which occur in molec-ular structures. It applies to the mathematical study ofthe beta-sheet models which appear in the protein fold-ing. The β sheet (sometimes called β-pleated sheet) is aform of regular secondary structure in proteins (as the mostwell-known form is the alpha helicoidal sheet). The exist-ing literature approximates the β sheet models by mini-mal surfaces (catenoidal surfaces). We will prove that theexisting model is neither mathematically nor chemicallyappropriate, and we will propose a different model basedon surfaces whose mean curvatures lie in intervals of theform (h− ε, h+ ε). Mathematical tools involved are basedon differential geometry, calculus of variations, numericalmethods and special functions.

Magdalena TodaDepartment of Mathematics and Statistics.Texas Tech Universitymagda.toda@ttu.edu

Modeling Coupled Gas Compositional Flow, Geo-chemical, and Thermal in Porous Media

Mojdeh DelshadUniversity of Texas at Austin

delshad@mail.utexas.edu

Simplified Mineralization Dynamics in Long-TermCO2 Storage

Geological CO2 storage relies upon long-term trapping ofCO2 within the storage formation. Knowledge of the effi-ciency of trapping mechanisms, of which the most perma-nent is carbon mineralization, is essential for risk analysis.Timescales of mineralization may be comparable to thetimescales of dissolution trapping due to convective mixing.We present results regarding the interaction between disso-lution trapping and mineralization trapping. We use sim-plified mineralization dynamics to efficiently explore sensi-tivity regarding the rate of mineralization.

Maria EleniusUni Researchmaria.elenius@uni.no

Helge HellevangUniversity of Oslohelge.hellevang@geo.uio.no

Sarah GasdaUniversity of North Carolina at Chapel Hillsarah.gasda@uni.no

Ivar AavatsmarkCenter for Integrated Petroleum ResearchUniversity of Bergenivar.aavatsmark@cipr.uib.no

A New Flow-Reactive-Transport Numerical Mod-eling Framework and Application to Co2 MineralCarbonation

Surveys of carbon reservoirs suggest that mineral carbon-ation is a stable long-term storage mechanism for CO2

in geologic formations. Simulation of carbonation entailsmodeling the coupled phase equilibrium, multiphase flow,species transport, and reaction processes. This presenta-tion describes a fully-coupled procedure for general flowand reactive-transport problems in a compositional sim-ulation framework, based on element conservations. Theprocedure, accomplished within Stanford General PurposeResearch Simulator, enables field-scale simulation of CO2

carbonation in deep saline aquifers.

Yaqing FanShell Oil Companyy.fan@shell.com

On the Transport of Particles in Oceanic Flows:Modeling, Theory, and Experiments

We study reduced models for transport of particle pollu-tants in the ocean. The particles transported by the fluidare modeled by another continuum phase, with models re-sembling dusty-gas or Eulerian ones adapted to the incom-pressible setting. Theoretical results and some numericalexperiments will be shown.

Luigi C. BerselliDipartimento di Matematica Applicata ”U.

126 GS13 Abstracts

Universita’ di Pisaberselli@dma.unipi.it

Matteo CerminaraScuola Normale Superiore, PisaIstituto Nazionale di Geofisica e Vulcanologiamatteo.cerminara@sns.it

Progresses and Challenges in Spectral Multido-main Simulations of Small-Scale Oceanic StratifiedFlow Processes

Following an overview of spectral multidomain penaltymethod (SMPM) fundamentals, we discuss the physicalinsights enabled by application of a singly non-periodicversion of SMPM to the simulation of select small-scaleoceanic stratified flow processes. We then present a recentmodification of SMPM for quadrilateral subdomains. Em-phasis is placed on the challenges, in terms of consistencyand preconditioning, resulting from the non-symmetric ma-trix in the iterative solution of the discretized pressurePoisson equation.

Peter DiamessisDepartment of Civil and Environmental EngineeringCornell Universitypjd38@cornell.edu

Central-Upwind Schemes for 2D Shallow WaterEquations

In this talk we will discuss central-upwind schemes for theshallow water equations. These equations are widely usedin many scientific applications related to modeling of wa-ter flows in rivers, lakes and coastal areas. Furthermore,many real world engineering applications require the use oftriangular meshes due to the complicated structure of thecomputational domains of the problems being investigated.Therefore the development of robust and accurate numer-ical methods for the simulation of shallow water models incomplex domains is an active challenging problem. In ourtalk we will discuss the recently developed central-upwindschemes for such models. We will demonstrate the perfor-mance of the proposed methods in a number of numericalexamples. This is joint work with J. Albright, S. Bryson,A. Kurganov and G. Petrova.

Yekaterina EpshteynDepartment of mathematicsUniversity of Utahepshteyn@math.utah.edu

Reconstruction of the Pressure in Long-Wave Mod-els with Constant Vorticity

The effect of constant background vorticity on the pres-sure beneath steady long gravity waves at the surface of afluid is investigated. Using an asymptotic expansion for thestreamfunction, we derive a model equation given in termsof the vorticity, the volume flux, total head and momentumflux. It is shown that for strong vorticity, the maximumpressure is not located under the wave crest, and the fluidpressure near the surface can be below atmospheric pres-

Henrik KalischUniversity of Bergenhenrik.kalisch@math.uib.no

Numerical Modeling of Oceanic Turbulent Mixing-Layers

We introduce elements for the mathematical and numericalanalysis of turbulence models for oceanic surface mixinglayers. Turbulent mixing-layer models are usually verti-cal first-order closure models, depending on the gradientRichardson number. We propose a model that allows tomanage mixing layer flows with horizontal perturbationsof the initial conditions. We perform a theoretical and nu-merical analysis of the model, and a comparison with ageneral model, based on the Primitive Equations.

Samuele RubinoUniversidad de Sevillasamuele@us.es

Multiscale Simulation of Reactive Flow and Trans-port in Porous Media

In this work we model single, multiphase, reactive, andnon-Newtonian flow at the pore and sub pore scales but de-velop multiscale techniques to bridge the pore and macro-scales. A more efficient, novel domain decompositionmethod is used for upscaling. The medium is decomposedinto hundreds of smaller networks (sub-domains) and thencoupled with the surrounding models to determine accurateboundary conditions. Finite element mortars are used as amathematical tool to ensure interfacial pressures and fluxesare matched at the interfaces of the networks boundaries.The results compare favorably to the more computation-ally intensive (and impractical) approach of upscaling themedia as a single model.

Matthew BalhoffICESThe University of Texas at Austinbalhoff@mail.utexas.edu

Adaptive Hybrid Models of Reactive Transport inPorous Media

Continuum-scale models of flow and transport in porousmedia rely on sets of assumptions and simplifications, andfail to describe experimentally observed phenomena when-ever such conditions are not satisfied. This is particularlytrue for highly localized phenomena, e.g. (bio-) geochem-ical reactive processes, in which poor mixing at the pore-scale often leads to a localized breakdown of macroscopicequations. In such systems the use of hybrid models, whichsolve pore-scale equations in a small portion of the com-putational domain and use their continuum counterpartseverywhere else, become imperative. A desirable featureof hybrid models is their ability to track where and whenin space and time to use pore-scale simulations, i.e. theiradaptability to time- and space-dependent phenomena. Inthis work, we construct criteria for adaptive hybridization,based on macroscopic dimensionless numbers. This ap-proach allows one to dynamically establish whether or nothybridization is needed at any instances in space and time,

GS13 Abstracts 127

by evaluating continuum-scale quantities only. Finally, weimplement the proposed adaptive hybridization scheme toreactive flow through a chemically heterogeneous planarfracture.

Ilenia BattiatoDepartment of Mechanical Engineering, ClemsonUniversityibattia@clemson.edu

On the Origin of Non-Fickian Transport in PorousMedia

The exact relationship between structure, velocity field andnon-Fickian transport in heterogeneous media has not beenfully understood. A novel methodology is developed thatpredicts transport on micro-CT images by using probabil-ity density functions (PDFs) of displacement and transittimes between image voxels, and relates it to PDF of lo-cal velocity. A key determinant for non-Fickian transportis the spread in velocity distribution, as demonstrated onbeadpack, sandstone and a range of complex carbonaterock.

Branko BijeljicDepartment of Earth Science and EngineeringImperial College Londonb.bijeljic@imperial.ac.uk

Martin J. BluntDepartment of Earth Science and EngineeringImperial Collegem.blunt@imperial.ac.uk

Pore-Network Modeling of Electrokinetic Flow andTransport in Microcapillaries

Electrokinetic transport porous media is a complex cou-pled phenomenon, which is highly influenced by surfacechemistry as well as transport of the ions in the microcap-illaries. After derivation of analytical relations for flow andtransport in a micro-capillary that include gradients of con-centration, pressure and electric potential, these relationsare solved numerically in a complex network. Effects ofheterogeneity of pore geometry and zeta potential on flowand transport have been studied.

Vahid Joekar-NiasarDepartment of Earth SciencesUniversity of Utrechtvahid.joekarniasar@shell.com

Simulation of Film and Droplet Flow on Smoothand Rough Wide Aperture Fractures usingSmoothed Particle Hydrodynamics

Gravity-driven flow in fractured porous media exhibitshighly dynamical interfaces and a wide range of intermit-tent flow processes ranging from adsorbed films to droplets,rivulets and wavy surface films. We present a free-surfaceSmoothed Particle Hydrodynamics model to simulate cap-illary forces dominated droplet and film flow on dry andprewetted wide aperture fracture surfaces. We demon-strate the various effects of wettability on the flow dynam-ics and show the influence of surface roughness on maxi-

mum Reynolds numbers.

Jannes KordillaGeoscientific CentreUniversity of Goettingenjkordil@gwdg.de

Alexandre M. TartakovskyPacific Northwest National Laboratoryalexandre.tartakovsky@pnl.gov

Tobias GeyerGeoscientific CentreUniversity of Goettingentgeyer@gwdg.de

Multiscale Simulation of Flow and Heat Transportin Fractured Geothermal Reservoirs with ImprovedTransport Upscaling

We present a framework for modeling and simulation offlow and heat-transport in fractured geothermal reservoirs,where fractures impact flow and transport at multiplescales. Flow in large-scale fractures are simulated explic-itly in the computational model, while flow in small-scalefractures and the porous media is upscaled. The link tothe fine-scale solution is kept to enable computation of ap-proximate fine-scale solutions. Based on the approximatefine-scale solutions, upscaling of the transport is improved.

Tor Harald SandveUniversity of BergenNorwaytor.harald.sandve@iris.no

Inga Berre, Eirik KeilegavlenUniversity of Bergeningab@mi.uib.no, eirik.keilegavlen@math.uib.no

Title Not Available at Time of Publication

Alifio GrilloPolythecnic of Turin, Italyalfio.grillo@polito.it

Space-Time Domain Decomposition For TransportIn Porous Media With Fractures

We consider nonoverlapping domain decomposition meth-ods for transport problems in porous media with frac-tures. The first approach uses the time dependent Steklov-Poincare operator and the second uses the optimizedSchwarz waveform relaxation. Each method enables differ-ent time steps in the subdomains. Both d-dimensional and(d− 1)-dimensional fractures (for a d-dimensional domain)are considered. Numerical results in 2D will be presented.

128 GS13 Abstracts

Thi Thao Phuong HoangINRIA Paris-Rocquencourt, FrancePhuong.Hoang Thi Thao@inria.fr

Caroline JaphetParis 13 university, Francejaphet@math.univ-paris13.fr

Modeling Subsurface Fractures Using Enriched Fi-nite Element Method

Enriched finite element method (EFEM) allows us to accu-rately model fractures without having to construct mesh tohonor geometries of fractures. In this talk, we will presenttwo applications of EFEM with improved formulations.The first one concerns rapid evaluation of well productiv-ity with fractured completions. Examples will be given onhow to use the new method to quantify the impact of non-Darcy effect for different configurations of fractured stimu-lation. The second application concerns predicting naturalfracture patterns under geological loading. The method tomodel fracture interaction in EFEM will be discussed.

Hao Huang, Jichao Yin, Rodrick Myers, Richard AlbertExxonMobil Upstream Research Companyhao.huang@exxonmobil.com, jichao.yin@exxonmobil.com,rodrick.d.myers@exxonmobil.com,richard.albert@exxonmobil.com

A Numerical Method for Two-Phase Flow in Frac-tured Porous Media with Non-Matching Grids

Two-phase flows in porous media are influenced by thepresence of fractures in many relevant applications. In-stead of refining the grid to capture the fractures, we rep-resent them as immersed interfaces, using a reduced modelfor the flow and suitable coupling conditions. We allowfor non matching grids between the porous matrix and thefractures to obtain a flexible method for realistic configu-rations. Numerical fluxes that yield an entropic and con-servative scheme are discussed.

Compressibility of Porous Materials with Com-pressible Fluids Using Thermodynamics

There are a variety of compressibilities for porous materi-als: jacketed, unjacketed, and pseudo-bulk are a few ex-amples. The relationship between these compressibilitiestraditionally do not account for the volume fraction. Herewe present how thermodynamics can be used to determinethe relationship between these compressibilities, the vol-ume fraction, and the compressibility of each phase.

Lynn S. BennethumUniversity of Colorado DenverLynn.Bennethum@cudenver.edu

Modeling Transport of Charged Colloids IncludingElectrochemically Induced Adhesive Interactions

In this talk, we present a pore scale model describing thetransport of charged colloids in a porous medium. Despitediffusion, convection and electrophoretic transport mecha-nisms, the considered model includes electrochemically in-duced adhesive interactions. The talk focuses on how tomodel these additional adhesive interactions which play animportant role in many applications.

Matthias HerzDepartment of MathematicsUniversity of Erlangenmatthias.herz@fau.de

Multiscale Modeling of Colloid and Fluid Dynamicsin Porous Media including an Evolving Microstruc-ture

We describe colloidal dynamics and fluid flow within aporous medium at the pore scale. The model consists ofthe NernstPlanck and Stokes equations including a forcingterm. Surface reactions result in an evolution of the mi-crostructure which is captured by a level set function. Ap-plying an averaging procedure in this framework, we obtainDarcys law and a convectiondiffusion equation with time-and space-dependent coefficients. The results are comple-mented by simulations of a heterogeneous multiscale sce-nario.

Nadja RayUniversity of Erlangen-Nurembergray@am.uni-erlangen.de

Tycho van Noorden, Florian Frank, Peter KnabnerDepartment of MathematicsUniversity of Erlangenvannoorden@math.fau.de, frank@math.fau.de,knabner@math.fau.de

Multiscale Adaptive Simulations of Concrete Car-bonation Taking into Account the Evolution of the

GS13 Abstracts 129

Microstructure

Concrete carbonation is a chemical degradation mecha-nism compromising the service life of reinforced concretestructures. Using a homogenization approach to upscalethe associated reaction–diffusion system given in a porousmedium, whose microstructure undergoes an evolution intime, an effective macroscopic limit model is obtained. Tolower the complexity of numerical simulations further, aneffiŒcient adaptive øfinite element scheme for the limitproblem is presented. The approach is generally applica-ble to reaction–diffusion problems in porous media.

Claus-Justus HeineUniversity of Stuttgartclaus-justus.heine@ians.uni-stuttgart.de

Christian Moeller, Malte A. PeterUniversity of Augsburgchristian.moeller@math.uni-augsburg.de,malte.peter@math.uni-augsburg.de

Kunibert SiebertUniversity of Stuttgartkg.siebert@ians.uni-stuttgart.de

Conceptual Multiscale Models for Flows in LayeredDeforming Media

We present sveral approaches to reduce computationalcomplexity of flow and deformation simulations in dou-ble porous media featured by local periodicity which is as-sumed in the “horizontal directions’ for each layer. Homog-enized models are obtained which result in the 3D-to-2Ddimensional reduction of the associated PDEs, while themicrostructure is fully 3D. We develop coupling conditionswhich enable us to combine models for several homoge-nized layers to approximate a 3D structure. Applicationsin tissue perfusion are discussed.

Eduard RohanDept. of Mathematics, Faculty of Applied SciencesUniversity of West Bohemiarohan@kme.zcu.cz

Vladimir LukesUniversity of West Bohemia, Pilsenlukes@kme.zcu.cz

Modelling Chemical Reactions in Porous Mediawith Particle Based Methods

We use a particle-tracking method to simulate several one-dimensional bi-molecular reactive transport experiments.In our numerical scheme, the reactants are representedby particles: advection and dispersion dominate the flow,and molecular diffusion dictates, in large part, the reac-tions. When compared to the solution of the advection-dispersion-reaction equation (ADRE) with the well-mixedreaction experiments and the particle-tracking simulationsagreed well showing 20% to 40% less overall product, whichis attributed to poor mixing. The poor mixing also leads tohigher product concentrations on the edges of the mixingzones, which the particle model simulates more accuratelythan the ADRE.

David A. Benson

Colorado School of Minesdbenson@mines.edu

Mixing Entropy and Reactive Solute Transport

Mixing processes affect reactive solute transport in fluids.In this work the transport equation for the entropy of areactive compound is derived and we show that the expo-nential of the Shannon entropy is an appropriate metricto quantify the interplay between mixing and reactive pro-cesses. The degree of uniformity of the solute distributionfor a reactive species and its rate of change are informativemeasures of physical and (bio)chemical processes and theircomplex interaction.

Gabriele ChiognaUniversity of Trento, Italygabriele.chiogna@ing.unitn.it

David HochstetlerStanford Universitydhochste@stanford.edu

Alberto BellinUniversita de Trentoalberto.bellin@ing.unitn.it

Peter K. KitanidisDept. of Civil and Environmental EngineeringStanford Universitypeterk@stanford.edu

Massimo RolleStanford Universitymrolle@stanford.edu

Characterization and Modeling Non-Fickian Dis-persion Triggered by Matrix-Diffusion in PorousMedia

Mobile-immobile mass transfer model implicitly states thatlarge scale non-Fickian dispersion is controlled by the mi-croscale properties of the media. This model has been ap-plied successfully to interpret tracer tests at many scalesusing a memory function (MF) as a sink/source term in theADE equation for describing the transient diffusive mech-anisms in the immobile domain. The MF is an intrinsiccharacteristic of the medium that can be calculated usinghigh-resolution 3D representation of the pore structure.

Phillipe GouzeUniversity of Montpellierphilippe.gouze@um2.fr

Diffusion and Reaction in Heterogeneous Media: AContinuous Time Random Walk Approach

Reaction kinetics in heterogeneous systems are differentfrom the ones observed in well-mixed reactors. We presentan approach to model reactive transport in complex me-dia based on a transport representation in terms of con-tinuous time random walks. In this framework, linear ki-netic sorption-desorption reactions are modeled as com-pound Poisson processes. More general chemical reactionsare quantified using a kinetic Monte-Carlo approach. This

130 GS13 Abstracts

method allows studying the impact of heterogeneity onanomalous diffusion and reaction behavior.

Dentz MarcoSpanish National Research Council (CSIC)marco.dentz@idaea.csic.es

The Architecture of Random Mixtures

The principles of scalar mixing in randomly stirred media,aiming at describing the overall concentration distributionof the mixture, its shape, and rate of deformation as themixture evolves towards uniformity are reviewed. Thenwe consider the fine structure of a scalar mixture advectedin a random, interconnected, frozen network of paths, i.e.a porous medium. We describe in particular the relevantscales of the mixture, the kinetics of their evolution, thenature of their interaction, and the scaling laws describingthe coarsening process of the concentration field as it pro-gresses through the medium, including its concentrationdistribution.

Emmanual VillermauxUniv de Provence, IRPHEMarseille, Francevillermaux@irphe.univ-mrs.fr

Modeling Arterial Walls As Multi-Layered Poroe-lastic Structure and Their Interaction with Pul-satile Blood Flow

We present a new model and two novel loosely coupledschemes modeling fluid-structure interaction between anincompressible, viscous fluid and a multi-layered structure,consisting of a thin elastic shell and a poroelastic medium.Elastodynamics of the thin shell is described by the linearlyelastic Koiter shell model, while the poroelastic medium ismodeled as a Biot system. We present the analysis andcomparison of the two methods, and numerical results.

Martina BukacUniversity of PittsburghDepartment of Mathematicsmartinab@pitt.edu

Paolo ZuninoUniversity of PittsburghDepartment of Mathematicspaz13@pitt.edu

A Rigorous Derivation of the Equations for theBiot-Kirchhoff-Love Poroelastic plate

We rigorously study limit behavior of the solution to quasi-static Biots equations in thin poroelastic plates as thethickness in x3 direction tends to zero. At Terzaghis timescale we obtain the norm convergence. The bending andthe pressure equations are coupled. Bending equation con-tains Laplacian of the pressure bending moment. The pres-sure equation has derivatives only in t and x3 and contains

the time derivative of the in-plane Laplacian of the verticaldeflection.

Andro MikelicInstitut Camille Jordan, Departement de MathematiquesUniversite Lyon 1Andro.Mikelic@univ-lyon1.fr

Anna Marciniak-CzochraUniversity of HeidelbergGermanyanna.marciniak@iwr.uni-heidelberg.de

Geomechanical Coupling Between PoroelasticReservoirs and Viscoelastic Cap Rocks: Applica-tion to Pre-Salt Geological Formations

We construct locally conservative numerical methods fortwo-phase immiscible flow in a strongly heterogeneousporoelastic rock underneath a saline formation composed ofhalite and anydrite displaying creep behavior with the vis-cous strain ruled by a nonlinear constitutive law of power-law type. Numerical simulations are presented of a water-flooding problem in a strongly heterogeneous carbonatedrock overlain by a salt dome lying between a two-well verti-cal arrangement showing the effects of viscoelasicity uponbreakthrough curves.

Marcio A. MuradNational Laboratory of Scientific ComputationLNCC/MCTmurad@lncc.br

Jesus ObregonNational Laboratory of Scientific ComputingLNCC/MCTalexei@lncc.br

Marcio BorgesNational Laboratory of Scientific ComputationLNCC/MCTPetropolismrborges@lncc.br

Maicon R. Correa, Luiz RadtkeNational Laboratory of Scientific ComputingLNCC, Brazilmaicon@ime.unicamp.br, luizcr@lncc.br

Multiscale Modelling and Analysis of Flow, Chem-ical Reactions and Mechanical Processes in ElasticPorous Media

Microscopic descriptions (at the pore scale) of flow, trans-port and reactions of substances, and their interaction withmechanics of the solid phase in porous media, lead to cou-pled systems of partial differential equations in complexgeometric structures. We derive an effective descriptiongiven by the quasi-static Biot system, coupled with theupscaled reactive flow. Effective Biot’s coefficients dependon the reactant concentration. Additionally to the weaktwo-scale convergence results, convergence of the energiesis proved.

Maria Neuss-RaduUniversity of Erlangen-NurnbergMathematics Department

GS13 Abstracts 131

maria.neuss-radu@am.uni-erlangen.de

Willi JagerUniversity of Heidelbergjaeger@iwr.uni-heidelberg.de

Andro MikelicUniversity of Lyon 1andro.mikelic@univ-lyon1.fr

A High-order, Fully-coupled, Upwind, CompactDiscontinuous Galerkin Method for Modeling ofViscous Fingering in Compressible Porous Media

We present a new approach for high-fidelity porous mediaflow simulation, based on a fully coupled, upwind, high-order discontinuous Galerkin formulation of miscible (com-pressible) displacement transport. The proposed methodis flexible on complex subsurface geometries and capturesthe strong interaction between pressure and transportedconcentrations in highly compressible media. It also showsvery low sensitivity to mesh orientation and its robustnessand accuracy are demonstrated in a number of compress-ible and incompressible multiphase flow problems.

Guglielmo ScovazziDuke Universityguglielmo.scovazzi@duke.edu

Hao HuangExxonMobil Upstream Research Companyhao.huang@exxonmobil.com

Hardware-aware optimization of SeisSol, an un-structured ADER-DG code.

In this talk we give an insight into advanced hardware-aware optimizations applied to SeisSol, a package for sim-ulation of seismic wave phenomena on unstructured grids,based on the discontinuous Galerkin method combinedwith ADER time discretization. We show how a rigorousenriched pre-compile phase leads to significant speedups.Especially code generation for small sparse matrix ker-nels, typical for discontinuous Galerkin schemes, is a keypoint enabling usage of advanced features on state-of-the-art hardware, such as the AVX-instruction set. We alsodiscuss memory access patterns for unstructured grids usedin SeisSol, such as element orders or grid-dependent accessfrequencies to a small number of flux matrices. Finallywe give an outlook to optimizations introducing hardwarerequirements already in the numerical method, which iscrucial to prepare SeisSol for next-generation supercom-puters.

Alexander BreuerTechnische Universitat MunchenDepartment of Informaticsbreuera@in.tum.de

Alexander HeineckeTU Munchenheinecke@in.tum.de

Sebastian RettenbergerTechnische Universitaet MuenchenDepartment of Informatics, Chair of Scientific Computing

rettenbs@in.tum.de

Bader MichaelTechnische Universitat MunchenDepartment of Informatics, Scientific Computingbader@in.tum.de

Christian PeltiesLudwig-Maximilians-Universitaet MuenchenUniversity Munichpelties@geophysik.uni-muenchen.de

Large-Scale Dynamic Earthquake Rupture Simula-tions with the Ader-Dg Method: Towards Simula-tion Based Seismic Hazard Assessment

We aim to understand ground-motion generation fromlarge-scale dynamic earthquake scenarios in 3D Earthstructure using the ADER-DG scheme. The method solvesthe spontaneous rupture problem with high-order space-time accuracy on unstructured tetrahedral meshes. To thisend, geometrically complex faults can be accurately dis-cretized and a high frequency content may be generated.The physical problem is challenging for current numericalmethods with respect to both algorithmic and computa-tional complexity, and thus requires advanced optimizationstrategies.

Alice A. GabrielLMU Muenchengabriel@geophysik.uni-muenchen.de

Atanas AtanasovTechnical University Munichatanasoa@in.tum.de

Vipin SachdevaIBM Research, AustinIBMvsachde@us.ibm.com

Luca PassoneKing Abdullah University of Science and Technologyluca.passone@kaust.edu.sa

Kirk E. JordanIBM T.J. Watson Researchkjordan@us.ibm.com

Geoffrey ElyArgonne National Laboratorygely@anl.gov

Tsunami Alert and Forecast Using a Massive Par-

132 GS13 Abstracts

allel Multiscale Model over French Polynesia

Over the last four years, one widespread tsunami oc-curred each year in Pacific Ocean which were observed ontide gages and coasts of polynesian islands. The FrenchPolynesia Tsunami Warning Center (CPPT), located onTahiti, used these last events to improve the accuracy ofthe tsunami height estimation. In this context, the lasttsunamis have been modelled over Pacific ocean to testthe accuracy and validate our new local forecast systemof tsunami height based on our model using a parallel im-plementation and our new computational capabilities (2.5Tflops). The water surface initialization has been com-puted from Okada’s formulation, using seismic parametersevaluated by CPPT. Tsunami propagation has been mod-elled by a finite-difference numerical model solving shallowwater equations. The model is implemented using the do-main decomposition technique in conjunction with messagepassing interface (MPI). The values of tsunami amplitudes,flow velocities and arrival times are compared to the ob-served data in French Polynesia.

Anthony Jamelot, Dominique Reymond

CEA/LDG Pamatai, Tahiti, French Polynesiajamelot@labogeo.pf, reymond.d@labogeo.pf

Helene HebertCEA,DAM,DIF F-91297 Arpajon Francehelene.hebert@cea.fr

The SeisSol Software Package for TsunamigenicEarthquake Simulations

We will present the SeisSol software package for the sim-ulation of tsunamigenic earthquakes. The dynamic earth-quake faulting and the subsequent seismic wave propaga-tion is solved simultaneously by a high order ADER-DGmethod implemented on unstructured tetrahedral meshes.The package provides a workflow with a concept for meshgeneration, pre- and postprocessing tools and solutionsfor visualization. To demonstrate the advantages of thescheme we will present a subduction earthquake scenario.

Alice A. GabrielLMU Muenchengabriel@geophysik.uni-muenchen.de

Alex HeineckeTU Muenchenheinecke@in.tum.de

Michael BaderTechnische Universitaet Muenchen

Department of Informaticsbader@in.tum.de

Martin KaeserGeo Risk Research, Munich Reinsurancemartin.kaeser@geophysik.uni-muenchen.de

Comparison of Open Source Porous Media Simula-tors for Reservoir Engineering Applications

Open-source code provides a chance for sustainable soft-ware development in the geosciences, being attractive foracademic institutions and industry. Recently, several open-source simulators have been developed for flow in porousmedia. This talk presents a detailed comparison of someof these simulators for reservoir engineering applications.By means of realistic field-scale scenarios, robustness, ef-ficiency and accuracy are compared by means of variousmeasures. All participating simulators are part of the OpenPorous Media Initiative, opm-project.org.

Kristin FlornesIRIS, Bergen, NorwayKristin.Flornes@iris.no

Fully Implicit Solvers for Matlab Reservoir Simu-lation Toolbox (MRST)

We present a framework for development of fully implicitsolvers based on automatic differentiation (AD) in theopen-source toolbox MRST. With an AD-class for auto-matically generating Jacobians, solver prototyping basi-cally boils down to writing down the residual equations.It also facilitates easy manipulation of Jacobians, essen-tial for preconditioning. As example we use the code foradjoint-based optimization of net-present-value for a real-istic case using the black-oil model.

Stein Krogstad, Olav MøynerSINTEF ICTStein.Krogstad@sintef.no, olav.moyner@sintef.no

Ensemble Kalman Filter Toolbox in Mrst

An open source Ensemble Kalman Filter (EnKF) modulewas developed for use with the Matlab-based reservoir tool-box MRST. The module can be used for rapid testing andprototyping of new algorithms and workflows for historymatching reservoir models to production or seismic data.This presentation will discuss the functionality included inthe module and show examples on both synthetic grids andEclipse corner point grids.

Olwijn LeeuwenburghTNO, The Netherlandsolwijn.leeuwenburgh@tno.nl

GS13 Abstracts 133

Flow Diagnostics on Stratigraphic Grids

We present a set of simple flow diagnostic tools that canbe used to assess the quality of upscaling and quantify un-certainty in reservoir characterization. The tools are basedon the computation of time-of-flight and stationary tracerdistribution using an Eulerian rather than a streamline for-mulation. The tools are available as a module in the open-source Matlab Reservoir Simulation Toolbox.

Upscaling of Fine Scale Geological Models for Non-Linear Flow Simulations

In this work some classical upscaling methods are extendedto the non-linear Forchheimer law. We consider the in-compressible and slightly compressible single phase steadystate filtration in anisotropic heterogeneous porous media.Our approach is local: the fine grid problem is solved inde-pendently on each subregion covering the coarse cell withsuitable boundary conditions. The fine solution is thenused to determine the coarse cell parameters locally on asingle coarse cell.

Eugenio AulisaDepartment of Mathematics and Statistics.Texas Tech Universityeugenio.aulisa@ttu.edu

Lidia BloshanskayaTexas Tech UniversityDepartment of Mathematics and Statisticslidia.bloshanskaya@ttu.edu

Akif IbragimovTexas Techakif.ibraguimov@ttu.edu

Multiscale Finite Volume Method For High-Contrast Heterogeneous Media

We study the mathematical properties of the MSFVmethod and detect the cause of its failure in presence ofhighly heterogeneous transmissibility fields. Local grid-and stencil-based treatments are proposed to resolve thislimitation in a general way. For several problems we showthat the results of our conservative MSFV are accurate andmonotone with no nonphysical peaks.

Hadi HajibeygiDelft University of TechnologyDept. of Geoscience and Engineeringhadih@stanford.edu

Yixuan WangStanford Universityyixuanw@stanford.edu

Theory and Software Concepts

Based on a mathematical abstraction layer for multiscalemethods such as the heterogenous multiscale method, mul-tiscale finite element methods and the localized reducedbasis multiscale (lrbms) method [Albrecht, F. et al., 2012.The Localized Reduced Basis Multiscale Method. In A.Handlovicova, Z. Minarechova, & D. Sevcovic, eds. Algo-ritmy 2012. Publishing House of STU, pp. 393–403.] weintroduce an interface-based software framework enablingexascale computing for multiscale methods. Additionallywe present recent results for the lrbms method.

Sven KaulmannUniversity of Stuttgartsven.kaulmann@mathematik.uni-stuttgart.de

Conditional Numerical Simulations of Flow andTransport in Porous Media

In this talk we compare the solutions of flow and transportmodels obtained by conditional simulations with MonteCarlo and stochastic collocation methods. We show thatfor both methods the conditioning helps to reduce the un-certainty of the solutions. We discuss a method of simu-lating the conditional random fields based on the uncondi-tional representation and provide the error estimates asso-ciated with the simulation of conditional random fields.

Veronika S. VasylkivskaDepartment of MathematicsOregon State Universityvasylkiv@math.oregonstate.edu

Mina E. OssianderMath DeptOregon State Universityossiand@math.oregonstate.edu

Multiscale Parameterization of Geologic Uncer-tainty

Xiao-Hui Wu, Larisa V. Branets, Yahan YangExxonMobil Upstream Research Companyxiao-hui.wu@exxonmobil.com,larisa.v.branets@exxonmobil.com,yahan.yang@exxonmobil.com

A Finite-volume Approach for Coupled Simula-

134 GS13 Abstracts

tions of Ice, Sediment, and Melt-water Transport

We present a finite-volume approach for simulating coupledice-related flow processes. The method employs explicittime marching and discrete cell interactions. Ice flow iscomputed using a second-order shallow-ice approximation(iSOSIA). The inherent benefit of the method relates pri-marily to the ease with which several types of earth surfaceprocesses may be simulated simultaneously. We illustratethe potentials of the approach by simple model scenariosrelated to the long-term dynamics of alpine glaciers.

David Lundbek Egholm, Christian Braedstrup, AndersChristensenDepartment of Geoscience, Aarhus University, Denmarkdavid@geo.au.dk, christian.fredborg@geo.au.dk,anders.damsgaard@geo.au.dk

Inverse Modeling of the Greenland Ice Sheet FlowDynamics: from Local Sensitivity to Large-ScaleModel Initialisation

Over the last two decades, the Greenland Ice Sheet hasbeen losing mass at an increasing rate, with an impor-tant contribution coming from acceleration and thinningof numerous outlet glaciers. Representing these changes inflow models is a challenge requiring the development of (i)grid refinement strategies to capture individually the nar-row outlet glaciers, (ii) efficient numerical schemes to solvethe appropriate flow equations and (iii) inverse methods toconstrain poorly known parameters. Here, we will presentdetails and applications of these recent developments fromlocal sensitivity analysis to large-scale model initialisation

Fabien Gillet-ChauletLaboratoire de Glaciologie et de Geophysiquede l’Environnemt, Grenoble, Francefabien.gillet-chaulet@lgge.obs.ujf-grenoble.fr

Olivier GagliardiniLGGE,Grenoble,FranceIUF,Franceolivier.gagliardini@ujf-grenoble.fr

Jerome MonnierMathematics Institute of Toulousejerome.monnier@insa-toulouse.fr

nathan martinIMT CNRS/INSA/UPS, Toulouse, France.nathan.mar7in@gmail.com

Catherine RitzLGGE,Grenoble,Francecritz@lgge.obs.ujf-grenoble.fr

Maelle NodetLJK / Universite Joseph Fourier Grenoble (France)INRIA Rhone Alpes, Francemaelle.nodet@inria.fr

Estimating the Ice Thickness of Mountain Glacierswith An Inverse Approach Using Surface Topogra-

phy and Mass-Balance

We present an inverse approach to estimate the ice thick-ness distribution within a mountain glacier, given transientsurface geometry and mass-balance. It is based on the min-imization of the surface topography misfit in the shallowice approximation. Neither filtering of the surface topogra-phy nor interpolation of the basal shear stress is involved.Novelty of the method is the use of surface topography andmass-balance only within a time-dependent Lagrangian ap-proach for moving-boundary glaciers.

Laurent MichelEcole Polytechnique Federale de LausanneLausanne, Switzerlandlaurent.michel@epfl.ch

Marco PicassoEPFL, Switzlerandmarco.picasso@epfl.ch

Daniel Farinotti, Andreas Bauder, Martin FunkVAW, ETHZ, Switzerlandfarinotti@vaw.baug.ethz.ch, bauder@vaw.baug.ethz.ch,funk@vaw.baug.ethz.ch

Heinz BlatterInstitute for Atmospheric and Climate ScienceETHZ, Switzerlandheinz.blatter@env.ethz.ch

Dynamic Effects and Hysteresis in Two-Phase Flowin Porous Media

We consider a model describing two-phase flow in porousmedia, where dynamic effects are taken into account in thedifference of the phase pressures(’tau term’).We investigatethe existence and uniqueness of weak solutions, startingwith the non-degenerate case and then extending to thedegenerate case . Then we study the convergence of nu-merical approximation schemes and the error estimates inthe two cases.

Xiulei CaoDepartment of Mathematics and Computer ScienceTU Eindhoven, NLx.cao@tue.nl

Hysteresis and Trapping in Two-Phase Flow inPorous Media

The parameters and parameter functions of classical for-mulations of two-phase flow in porous media - the relativepermeability saturation relationship, the capillary pressure- saturation relationship, and the associated residual sat-urations - show path dependence, i.e. their values dependnot only on the state variables but also on their drainageand imbibition history. In my talk I will focus on hysteresisof the standard model and illustrate mathematical impli-cations, modeling challenges and possible applications.

GS13 Abstracts 135

A Componnt-Based Eulerian-Lagrangian Formu-lation for Multiphase Multicomponent Flow inPorous Media

Hong WangUniversity of South CarolinaDepartment of Mathematicshwang@math.sc.edu

Estimation of Discrete Geologic Facies Distribu-tions from Production Data Using ProbabilityMaps

Conditioning complex geologic facies models to nonlinearflow data leads to a discrete parameter estimation problem.We introduce a probability conditioning method (PCM)that, instead of directly estimating facies distribution, usesthe flow data to infer spatial facies probability maps. Theprobability maps are then used to guide facies simulation.We extend the proposed PCM approach to a Bayesian mix-ture model formulation for conditional simulation undermultiple plausible prior facies connectivity models.

Behnam JafarpourChemical and Electrical EngineeringUniversity of Southern Californiabehnam.jafarpour@usc.edu

Morteza KhodabakhshiTexas A&M Universitykhodabakhsh. @ mail.com

Updating Large-Scale Geological Structures andApplication to Shallow-Marine Environments

Accurate description of dominant large-scale geologicalstructures in petroleum reservoirs are essential for im-proved hydrocarbon recovery. In this talk we discuss chal-lenges related to updating of these features. Further, weshow an application where the ensemble Kalman filter isused to update facies boundaries and petrohpysical param-eters in a field with shallow-marine environment character-istics. The methodology is based on a parameter transfor-mation that ensures better agreement with the necessaryGaussian assumptions.

Rolf Lorentzen, Geir NævdalIRISrjl@iris.no, gen@iris.no

Ali ShafieiradStatoilseys@statoil.com

Channelized Reservoir Estimation using EnKF. AProbabilistic Approach

In this study we estimate the locations of facies types thatoccur in the reservoir domain. We introduce a new objectnamed ”signed probabilities field”, and probabilities areused as distances from two instances represented by 1 and0. Then, the ensemble Kalman filter is applied for the ob-

jects of this space and with an inverse function we rebuildthe facies distribution. We present two examples with dif-ferent types of complexity, both channelized reservoirs.

Bogdan SebacherTU Delftbogdansebacher@yahoo.com

Remus Hanearemus.hanea@tno.nltu delft

Arnold HeeminkDelft University of Technologya.w.heemink@ewi.tudelft.nl

Multi-Level Estimation of a Layered Subsurfacefrom Sea Floor Electromagnetic Data

We aim to identify large-scale geological structures withdifferent electric conductivities using seafloor electromag-netic data. An implicit representation of the parameterstructure related to level-set parameterization is applied toreduce the number of parameters while maintaining struc-tural flexibility. To quantify the model uncertainties weuse ensemble-based estimation methods. We balance datafit and stability using a multi-level regularization, while anew technique called shape priors is applied to incorporategeological realism.

Svenn TveitUni CIPRDept. of Mathematics, U. of Bergensvenn.tveit@uni.no

Shaaban Ali Bakr, Martha LienUni CIPRshaaban.bakr@uni.no, martha.lien@uni.no

Trond MannsethCentre for Integrated Petroleum ResearchUniversity of Bergen, Norwaytrond.mannseth@uni.no

Vanishing Cap-illarity Solutions of Buckley-Leverett Equation inMulti-Layer Porous Medium and Their Approxi-mation by a Convergent Phase-by-phase UpstreamScheme.

We present mathematical and numerical tools for approx-imating two-phase flow models in porous media that con-sist of different rock types. We study situations where thecapillary effects can be neglected within each rock; butat the junctions between rocks, capillarity effects shouldbe carefully taken into account. From the mathemati-

cal viewpoint, Buckley-Leverett equation with neglectedcapillarity admits many different weak solutions. Follow-ing Kaasschieter (Comput. Geosci., 1999), using a theoryfor discontinuous-flux conservation laws we deeply investi-gate vanishing capillarity limits in dimension one and pointout some wrong interpretations of the Kaasschieter’s re-sult that appeared in the literature. We derive a simple

procedure that selects the physical solution. We use it todesign efficient finite volume schemes in multiple space di-mensions. In particular, we claim that the phase-by-phase

136 GS13 Abstracts

upstream scheme can be adapted to the heterogeneous set-ting in such a way that it does converge to the physicallyrelevant vanishing capillarity solution.

Boris AndreianovLaboratoire de MathematiquesUniversite de Franche-Comteboris.andreianov@univ-fcomte.fr

Konstantin BrennerLaboratoire Jean-Alexandre DieudonneUniversite de Nicekonstantin.brenner@unice.fr

Clement CancesLab. Jacques-Louis LionsParis 5eme, Francecances@ann.jussieu.fr

Multi-Phase Multi-Component Flow in Heteroge-neous Porous Media

Natural porous media often show a pronounced heterogene-ity, which not only influences the permeability but also rel-ative permeability and capillary pressure saturation curves.This is of particular importance for applications like soilphysics. We present an approach for the numerical solutionof Richards’ equation and of multi-phase multi-componentflow based on a capillary pressure – phase pressure formu-lation. Application relevant test cases are solved with aself-centred Finite-Volume scheme and the results are dis-cussed.

Rebecca NeumannInterdisziplinares Zentrum fur WissenschaftlichesRechnen (IUniversitat Heidelberg, Germanyrebecca.neumann@iwr.uni-heidelberg.de

Finite Volume Discretizations of Two Phase DarcyFlows with Discontinuous Capillary Pressures

This talk deals with the extension of the finite volume ver-tex approximate gradient scheme to take into account dis-continuous capillary pressures for two phase Darcy flowson general meshes. Our approach is based on the choice ofthe phase pressures as primary unknowns at the verticeswhich allows for discontinuous saturations at the interfacebetween different rocktypes. The scheme is shown to con-verge on a simplified model and numerical tests exhibit itsefficiency on general meshes.

Roland MassonUniversity of Nice Sophia Antipolisroland.masson@unice.fr

Robert EymardUniversity Paris Eastrobert.eymard@univ-mlv.fr

Cindy GuichardUniversity of Nice Sophia Antipolisgucindy.guichard@unice.fr

Raphaele HerbinUniversity of Aix-Marseilleherbin@cmi.univ-mrs.fr

Discontinuous Galerkin Method for Two-phaseFlows in Heterogeneous Porous Media with Cap-illary Barriers

We present an accurate discontinuous Galerkin methodwith low numerical dispersion for two-phase immiscible in-compressible flows in heterogeneous porous media with adiscontinuous capillary field. Implicit Euler scheme is usedfor the saturation equation and the total velocity is re-constructed from the discontinuous Darcy flux in a RTNspace. The non-linear interface conditions are enforcedweakly through an adequate design of the penalties onjumps of the global pressure and the saturation at inter-face.

Igor MozolevskiFederal University of Santa Catarinaigor.e.mozolevski@gmail.com

Alexandre ErnUniversite Paris-EstCERMICS, Ecole des Pontsern@cermics.enpc.fr

Luciane SchuhFederal University of Santa Catarinaluciane floripa@yahoo.com.br

Nonlinear and Nonlocal: Combined Effects on Re-actions

Many transport processes in the subsurface have beenshown to be well modeled by equations that are nonlocalin space and or time. Further, many processes, includingchemical reactions require a nonlinear modelling approach.In this talk we explore the influence of nonlocal phenomenain nonlinear systems as they pertain to chemical reactionsin porous media.

Diogo BolsterDepartment of Civil Engineering and Geological SciencesUniversity of Notre Damebolster@nd.edu

Multiscale Methods for Fluid-Structure Interactionwith Applications to Poroelasticity

Modeling Fluid-Structure Interaction (FSI) is a compli-cated task in its own right, but when dealing with com-plicated microstructure with many scales direct numeri-cal simulation is often impossible. To circumvent this dif-ficulty, using a two-scale homogenization approaches, weare able to obtain a nonlinear effective poroelastic model.

GS13 Abstracts 137

Unlike in the linear poroelastic setting, the effective coeffi-cients are nonlinearly coupled to micro-scale cell equations.We present computational techniques to deal with comput-ing the effective coefficients off-line.

Donald BrownTexas A&M Universitydonaldbrowdr@gmail.com

Victor CaloKAUSTvmcalo@gmail.com

Peter PopovBulgarian Academy of Sciencesppopov@parallel.bas.bg

Langevin Model for Anomalous Reactive Transport

Under certain conditions, effective transport equations failto describe accurately reactive transport. In this presenta-tion, a stochastic reduction model based on the Langevinapproach will be presented. Numerical discretization andaccuracy of the resulting stochastic equations will be dis-cussed in the context of anomalous transport with mixingcontrolled bimolecular reactions.

Alexandre M. TartakovskyPacific Northwest National Laboratoryalexandre.tartakovsky@pnl.gov

Quantifying Mixing of Passive Scalars in Heteroge-neous Porous Media Flow using Lagrangian Statis-tics

The role of kinematics in increasing mixing efficiency hasbeen topic of intense research in the past. Mixing con-sists of stretching and folding of material lines and sur-faces, which serve to homogenize the scalar distribution.Mapping these kinematical properties onto mixing mea-sures can help to further our understanding of the systemand provide better predictions. In this talk, we quantifymixing measures as a function of the kinematical mecha-nisms such as straining and shearing on large-scale trans-port. Our work differs from previous ones in the sensethat we focus on investigating the Lagrangian statistics ofthe spatially variable kinematical measures experienced bysolute parcel in enhancing the overall mixing. We mapmixing and transport patterns with the spatial structureof velocity fields in terms of its deformation counterparts.Our results illustrate the appearance of coherent structureswhen we map the spatially varying velocity field onto thekinematical measures. We hypothesize that analyzing theLagrangian statistics of kinematical measures and its cor-relation properties can help understand their consequencesin mixing of passive scalar. In particular, quantify the cor-relation properties (auto-correlation and cross-correlation)of the different deformation components.

Felipe de BarrosPolitecnica de Catalunyafbarros@usc.edu

Tanguy Le BorgneUniversity of Rennes, Francetanguy.le-borgne@univ-rennes1.fr

Marco DentzIDAEA, Spanish National Research Council (CSIC)marco.dentz@idaea.csic.es

A Water-Hydrogen Gas-Liquid Flow FormulatedAs a Complementarity Problem

We consider a two-phase –liquid-gas– two-component –hydrogen-water– system in a porous media flow. Wateris only in the liquid phase and hydrogen can be in thegas phase or dissolved following Henry’s law. This prob-lem arose from the simulation of the migration of hydrogenproduced by the corrosion of metallic containers in a deepunderground repository of nuclear waste. It is solved usinga complementarity formulation and a Newton-min method.

Ibtihel Ben Gharbia, Jean Charles GilbertINRIA-Rocquencourtibtihel.ben gharbia@inria.fr, jean-charles.gilbert@inria.fr

Presence of Fluid Phases as a Non-Linear Comple-mentarity Problem

Partly because of phase transitions, miscible fluid flows inporous media tend to be numerically difficult. This talkwill present an approach to explicitly deal with phase tran-sitions in the system of equations. For this, the transitionconditions are formulated as a set of local inequality prob-lems. We will briefly discuss how this approach can be usedfor numerical models and flash calculations and compareit to previous approaches by means of several numericalexamples.

Andreas LauserUniversitat Stuttgart, Germanyandreas.lauser@iws.uni-stuttgart.de

A General Model for Two-Phase Flow in Terms ofMultiple Complementarity Conditions

We present the formulation and examine the properties ofa general mathematical model for compositional two-phaseflow in porous media. We discuss the proper choices ofprincipal variables and subsequent static (flash) equationsallowing for any (dis)appearance of one of the phases with-out the need of variable switching or unphysical quantities.The formulation in terms of complementarity conditions al-lows for an efficient and stable solution by the semismoothNewton’s method.

Estelle MarchandDepartment Mathematik, AM1Friedrich-Alexander-Universitaet Erlangen-Nuernbergmarchand@am.uni-erlangen.de

138 GS13 Abstracts

Peter KnabnerFriedrich-Alexander University Erlangen-Nurenberg,GermanyDepartment of Mathematicsknabner@am.uni-erlangen.de

Torsten MullerUniversitaet Erlangen-Nuernbergtmueller@am.uni-erlangen.de

Analysis and Numerical Approximation ofMethane Hydrates Model

Modeling of formation and dissociation of methane hy-drates is important for energy and climate studies. Thenonlinear degenerate PDE model has to account for multi-ple phases and solubility constraints. An appropriate for-mulation using monotone operator techniques leads to well-posedness results extending those for a porous-mediumequation and Stefan problem. In turn, we can take ad-vantage of complementarity constraints to get convergenceresults comparable to those for Stefan problem but with asuperior solver performance.

Ralph Showalter, Malgorzata Peszynska, Nathan L.Gibson, F. Patricia MedinaDepartment of MathematicsOregon State Universityshow@math.oregonstate.edu,mpesz@math.oregonstate.edu,gibsonn@math.oregonstate.edu,medinaf@math.oregonstate.edu

Adaptive Discontinuous Galerkin Simulations ofShallow Water Flow

Building on the work of Giraldo et al. (2002), we intro-duce an adaptive triangular Discontinuous Galerkin modelfor solving the two-dimensional shallow water equations.Accurate Riemann solvers and limiters ensure a correcthandling of interfaces between wet and dry cells, whilethe adaptive mesh, which is created using the library am-atos (Behrens et al. (2005)), reduces computational costswithout effecting the precision. Several idealized testcasesdemonstrate the method’s accuracy and efficiency.

Nicole Beisiegel, Jorn BehrensKlimaCampus, University of Hamburgnicole.beisiegel@zmaw.de, joern.behrens@zmaw.de

Comparing a DG Dynmaic Core for Local AreaWeather Prediction with the Operational COSMOModel

We introduce a dynamic core based on the DiscontinuousGalerkin method, implemented within the Dune softwareframework (www.dune-project.org/fem). Special mecha-nisms are included for advection dominated flow and forincluding local grid adaptation. We first study the effi-ciency, and scalability of the code. To further investigatethe effectiveness and efficiency of the code, we compare itwith the operational COSMO model in cooperation withthe German Weather service.

Andreas Dedner

University of Warwicka.s.dedner@warwick.ac.uk

Discontinuous Galerkin Methods for Adaptive At-mospheric Flow

We present higher order discontinuous Galerkin (DG)methods for adaptive atmospheric flow problems. Adap-tive DG methods will be applied to standard test casesfor atmospheric flow and different adaptation indica-tors will be discussed. The implementation of the DGmethods is based on the software package DUNE-FEM(dune.mathematik.uni-freiburg.de) which is a module ofDUNE (www.dune-project.org). The numerical results willbe accompanied by a short presentation of implementationdetails such as dynamic load balancing.

Robert KloefkornUniversity of Freiburgrobertk@ucar.edu

A Semi-Implicit, Semi-Lagrangian, P-AdaptiveDiscontinuous Galerkin Method for the RotatingShallow Water Equations on the Sphere

As a first step towards construction of a DG based dy-namical core for high resolution atmospheric modelling, asemi-implicit and semi-Lagrangian Discontinuous Galerkinmethod for the SWE is proposed and analysed. Themethod is equipped with a simple p-adaptivity criterion,that allows to adjust dynamically the number of degreesof freedom employed. Numerical results in the frameworkof standard idealized test cases prove the accuracy and ef-fectiveness of the method even at high Courant numbers.

Giovanni TumoloICTP, Trieste, Italygrumolo@ictp.it

DuMux As a Versatile Tool for Special Core Anal-ysis

An important problem in the interpretation of specialcore analysis (SCAL) laboratory data is that during rela-tive permeability measurements a strong interference existswith the capillary forces. To unravel this interference, sim-ulations of the experiments are necessary. The presentationhighlights how DuMux has been adapted to simulate SCALexperiments, significantly improving the business impact ofSCAL measurements. A web-based user interface to Du-Mux is made available that can be used free of charge.

Jos G. MaasTNO, The Netherlandsjgmaas@euronet.nl

Albert HebingPanTerra GeoConsultantsa.hebing@panterra.nl

GS13 Abstracts 139

Multiscale Simulation of Flow in Fractured PorousMedia using MRST

Flow and transport in fractured porous media involves pro-cesses on a continuum of scales, and a successful simulationstrategy requires an adequate representation of the scales.We propose a two-level method, where dominating frac-tures define the coarse model. Then the long-range corre-lations in the problem are represented in the coarse modeland, moreover, fractures give a physical interpretation ofthe tangential approximation often applied to determineboundary conditions for localized problems providing thebasis functions.

Tor Harald SandveUniversity of BergenNorwaytor.harald.sandve@iris.no

Opm Simulation of Polymer Injection

The Open Porous Media (OPM) Initiative provides a set ofopen-source GPL licensed tools centered around the simu-lation of flow and transport of fluids in porous media. Inthis talk we will give an overview of the capabilities of OPMand focus on the Enhanced Oil Recovery module. We willshow simulation of polymer injection into a reservoir withheavy oil. Numerical results will be compared with outputfrom commercial tools.

Ove SvareidIRIS, Bergen, Norwayove.saevareid@iris.no

Atgeirr F. RasmussenSINTEFatgeirr@sintef.no

Kristin M. FlornesIRISkristin.flornes@iris.no

MPFA on Adaptive Parallel Grids with Applica-tions to Reservoir Engineering

Large scale simulation of flow through porous media withhigh spatial resolution of materials and processes requireaccurate but efficient numerical solvers. One developmentbranch in the simulator DuMux addresses this problem bya bundle of sequential (IMPET) solvers which allow the useof non-conforming adaptive and/or parallel grids. Accurateflux approximation on hanging nodes is achieved by MPFAmethods and efficient solution of the linear system by aparallel AMG solver.

Markus WolffUniversity of StuttgartGermanymarkus.wolff@iws.uni-stuttgart.de

Benjamin FaigleUniversity of Stuttgartbenjamin.faigle@iws.uni-stuttgart.de

Intercomparison Efforts: An Overview

Stefan KolletMeteorological InstituteUniversity of Bonnstefan.kollet@uni-bonn.de

Intercomparison of Integrated Hydrologic Models

Reed M. MaxwellDepartment of Geology and Geologic EngineeringColorado School of Minesrmaxwell@mines.edu

Intercomparison of Geochemical Reactive Trans-port Models

Carl SteefelLawrence Berkeley National Laboratorycisteefel@lbl.gov

Intercomparison of Coupled Hydrologic Atmo-spheric Models

Mauro SulisMeterological InstituteBonn Universitymsulis@uni-bonn.de

Weak Galerkin Methods for Darcian flow: Hetero-geneity and Anisotropy

Guang LinPacific Northwest National Laboratoryguang.lin@pnnl.gov

Connection and Differences of WGFEMs andOther Finite Element Methods

James LiuDepartment of MathematicsColorado State Universityliu@math.colostate.edu

140 GS13 Abstracts

Guowei WeiDepartment of MathematicsMichigan State Universitywei@math.msu.edu

Weak Galerkin Finite Element Methods forHelmholtz Equations

Shan ZhaoDepartment of MathematicsUniversity of Alabamaszhao@bama.ua.edu

Pore-Scale Modeling of Multiphase ReactiveTransport with Phase Transitions and Dissolu-tion/precipitation Reactions

We present a pore-scale model for simulating multi-phase reactive transport processes including phase transi-tions and dissolution/precipitation reactions. The modelis based on the lattice Boltzmann method (LBM) andcombines the single-component multiphase Shan-ChenLB model, the mass transport LBM, and the dissolu-tion/precipitation model. Additional schemes are devel-oped to handle reactive and moving boundaries with com-plex geometries, to account for liquid/vapor phase transi-tion, and to guarantee mass and momentum conservationin a closed system.

Qinjun KangDivision of Earth and Environmental SciencesLos Alamos National Laboratoryqkang@lanl.gov

Bruce RobinsonLos Alamos National Laboratoryrobinson@lanl.gov

Li ChenXi’an Jiaotong Universitylichen@lanl.gov

Pore Scale and Multiscale Modeling Using LBM

We use GeoDict to generate geometries for representativeelementary volumes of real porous medias. The pore-scaleflows inside those geometries are simulated by the efficientLBM based on the N-S equation and macroscopic proper-ties are calculated. An efficient upscaling strategy is em-ployed to reduce the CPU time of micro- and macro-scalecomputations.

Jun LiKing Abdullah University of Science and TechnologyCenter for Numerical Porous Medialijun04@gmail.com

Victor M. Calo

Applied Mathematics and Computational ScienceKing Abdullah University of Science and Technologyvictor.calo@kaust.edu.sa

Oleg IlievFraunhofer Institute for Industrial MathematicsGermanyoleg.iliev@itwm.fraunhofer.de

Hybrid Multiscale Methods in Porous Media

One of the most significant challenges facing hydrogeologicmodelers is the disparity between those spatial and tempo-ral scales at which fundamental processes can best be un-derstood and quantified (e.g., microscopic to pore scales,seconds to days) and those at which practical model pre-dictions are needed (e.g., plume to aquifer scales, years tocenturies). We review a range of approaches to this chal-lenge, focusing on methods that directly integrate modelsdefined at multiple distinct scales.

Timothy D. ScheibePacific Northwest National Laboratorytim.scheibe@pnnl.gov

Accounting for Saturation History in Image-BasedPore-Scale Modeling of Two-Phase Flow

Multiphase flow behavior depends on saturation historyin many situations, which poses problems for traditionalDarcy-scale models (which treat the parameters as statefunctions of saturation) and also for pore-scale models thatemploy periodic boundary conditions (saturation cannotevolve naturally from the physics). In this paper we presenta pore-scale algorithm for dynamic two-phase flow that op-erates on non-periodic domains using pressure gradient andinlet fractional flow as boundary conditions. This enablesthe model to be used to study a wider variety of multiphaseflow conditions and to couple the algorithm to continuummodels.

Karsten ThompsonDept Petroleum EngineeringLouisiana State Universitykarsten@lsu.edu

Large-Scale Computations of Flows with Inertiaand Anisotropy Based on Micro-Imaging Data

Based on computational solutions of Navier-Stokes equa-tions in geometries representing porous media at a porescale, we study flows for a wide range of velocities. Ourmain focus is on performing simulations on voxel-basedmicro imaging real 3D data sets. Compared to syntheticgeometries, this brings challenges due to size, data resolu-tion, and complexity of structures. We propose a practicalpower-based fully anisotropic non-Darcy model at corescalewith parameters computed by upscaling.

Anna Trykozko

GS13 Abstracts 141

ICM - Interdisciplinary Centre for Mathematical andComputata.trykozko@icm.edu.pl

Local Time-Stepping and High-Order Discretiza-tion for Wave Propagation

We present a local time-stepping method combined with ahigh-order spectral element spatial discretization, for seis-mic wave propagation on locally refined meshes. Thisspace-time discretization is fully explicit. Local time-stepping methods however reduce the severe stability re-striction of explicit time-stepping scheme. The coarse andfine part of the mesh is here determined by the relationamong the mesh-size h and the polynomial order N. Nu-merical experiments illustrate the efficiency of the proposedmethod.

Loredana GaudioUniversity of Baselloredana.gaudio@unibas.ch

Marcus J. GroteUniversitat Baselmarcus.grote@unibas.ch

Seismic Elastic Modeling for Seismic Imaging

We shall discuss the pros and cons for forward modelingof elastic waves considering volumetric methods, boundaryintegral approaches and asymptotic formulations. Finitedifference methods are efficient. However, they suffer fromlimitations not met by finite element methods. Boundaryintegral approaches are quite efficient especially using fastmoment methods although simple heterogeneities shouldbe considered between boundaries. Asymptotic methodshave not met too much attention when considering fullwaveform inversion. We may see why.

Jean VirieuxISTerreUniversity Joseph Fourierjean.virieux@ujf-grenoble.fr

Romain BrossierISTerreromain.brossier@ujf-grenoble.fr

Stephanie ChaillatPOems-ENSTAstephanie.chaillat@ensta-paristech.fr

Anton A. DuchkovIPGG SB RAS and Novosibirsk State Universityduchkovaa@ipgg.nsc.ru

Vincent EtienneGEOAZURUniversity Nice - CNRSetienne@geoazur.unice.fr

Bruno LombardLMAlombard@lma.cnrs-mrs.fr

Stephane OpertoGEOAZURCNRSoperto@geoazur.obs-vlfr.fr

Aleksander SerdyukovIPGGaleksanderserdyukov@yandex.ru

High-Order High-Throughput Numerical Methodsfor High-Contrast Seismic Imaging

We will discuss numerical and computational issues driv-ing research into high-resolution methods for accurately re-solving wave propagation in high-contrast media. In par-ticular we will compare accuracy and efficiency of masslumped finite elements, spectral elements, and discontin-uous Galerkin based solvers for acoustic and elastic wavescattering problems. We will discuss the structure of themethods and how this relates to their parallel scalabilityon modern hardware accelerators.

Timothy WarburtonDepartment of Computational And Applied MathematicsRice Universitytimwar@rice.edu

David MedinaRice Universitydmedina@rice.edu

Amik St-CyrComputation and Modeling,Shell International E&P, Inc.amik.st-cyr@shell.com

Modeling Biofilm Formation Within MicrofluidicChannels

Despite multiple diseases causing widespread damage tothe citrus, wine, and other fruit industries, there has beenlittle attention paid to modeling biofilm development andprogression of many plantal bacterial infections. A multi-phase modeling framework will be used to examine the dy-namic behavior and fluid/structure interactions of biofilmcolonization within microfluidic channels. Linear stabilityanalysis will be used to determine potential causes and ten-dencies of a robust, regular spatial patterning visualized ina laboratory setting.

Matthew Donahue, Nick CoganDepartment of MathematicsFlorida State Universitymdonahu@gmail.com, cogan@math.fsu.edu

Leonardo de La FuenteDepartment of Entomology and Plant PathologyAuburn Universitylzd0005@auburn.edu

Mark E. WhiddenFlorida State University

142 GS13 Abstracts

mwhidden@math.fsu.edu

Modeling of Bacterial Growth, Adhesion andTransport in Porous Media

We introduce a numerical simulator for multiphase multi-component reactive flow in porous media, which is able toconsider simultaneously multiphase flow, component trans-port, phase exchange and microbiological processes. Theobserved behaviour of Escherichia coli like growth, adhe-sion and biofilm formation onto sand grains was added tothe simulator. The results of numerical simulations of E.coli growth and transport in the capillary fringe, with nu-trient supply under steady-state and transient flow condi-tions are finally compared to the experimental data.

Pavel HronIWRUniversity of Heidelbergpavel.hron@iwr.uni-heidelberg.de

Daniel JostKarlsruhe Institute of Technologydaniel.jost@kit.edu

Upscaling of Thin Layer Flows Involving Reactionsat Moving Solid-Fluid Interfaces

We consider pore scale models for reactive porous mediaflows, with particular focus on the case when the reactionproduct deposits in layers having non-negligible thicknesswhen compared to the pore size. This leads to modelsinvolving moving interfaces between the fluid and the de-posited layer. After addressing some modeling details, weconsider a simplified geometry for which we derive upscaledmodels. These results are further extended to transportdominating diffusion, and to biofilm growth.

Kundan KumarUniversity of Texas at Austink.kumar@gmail.com

Tycho van NoordenComsol B.V.t.l.v.noorden@gmail,com

Remediation in Porous Media by Bacterial Chemo-

taxis and Bioclogging

We model the degradation of pollutants in porous mediaby chemotactically moving bacteria that react with thecontaminants. Chemotaxis describes the influence of thelocomotion of organisms toward or away from the concen-tration gradient of a chemical species. A second species ofbacteria can form strong biofilms which can be used as bio-barriers to restrict the flow of the pollutants. Concerningthe corresponding system of PDEs we discuss some analyt-ical results and numerical simulations.

Raphael SchulzDepartment of MathematicsUniversity of Erlangenraphael.schulz@math.fau.de

Interaction of Reactive Flow with Solid Phase,Leading to Changes in Volume and MechanicalProperties - Mathematical Modelling and Simula-tion

The interaction of reactive flow with solid phase is an im-portant aspect in various applications, e.g. plaque forma-tion in blood vessels. In this talk, we formulate a model todescribe this process. This includes the interaction betweenflow and solid, and the penetration of chemical species inthe solid phase. Numerical simulations illustrate changesin volume of the solid phase, and increase stress values.

Yifan YangIWRUniversity of Heidelbergyifan.yang@iwr.uni-heidelberg.de

Maria Neuss-RaduUniversity of Erlangen-NurnbergMathematics Departmentmaria.neuss-radu@am.uni-erlangen.de

Miscemetry in Reactive Transport

Simulation of groundwater flow and transport relies on up-scaling fluid dynamics and linked reactive processes spec-ified at pore- or column-scales. Upscaling failure has ledmany to refocus on ”mixing measures” as proxies for re-actions. I review this approach as one of calculating theexposure-time of one solute to another, and develop (eule-rian) equations governing the evolution of a solute overspace, time, and mixing extent. Limitations associatedwith transition state theory are introduced.

Tim GinnUniversity of California at Davistrginn@ucdavis.edu

Scaling of Convective Mixing in Porous Media

Convective mixing in porous media results from aRayleigh–Benard-type instability resulting from a higherdensity fluid mixture overlaying a light fluid. Here we studythe scaling of dissolution fluxes by means of the varianceof concentration and the scalar dissipation rate. The fun-damental relations among these three quantities allow usto show that the classical model of convective mixing inporous media exhibits, in the regime of high Rayleigh num-

GS13 Abstracts 143

ber, a dissolution flux that is constant and independent ofthe Rayleigh number. Our findings point to the need foralternative explanations of recent nonlinear scalings of dis-solution flux observed experimentally.

Juan J. HidalgoMIT, Boston, USAjuanj.hidalgo@idaea.csic.es

Probability Density Function of Concentration inPorous Media

We study the mixing of a scalar line transported in a two-dimensional porous media under heterogeneous advectionand diffusion. We propose a theoretical framework to quan-tify the overall concentration distribution, predicting itsshape and rate of deformation as it progresses towards uni-formity. Analytical expression for the temporal scaling ofthe concentration moments and the scalar dissipation rateare derived for all times. High resolution numerical simula-tions of flow and transport in heterogeneous permeabilityfields provide a detailed quantification of concentration dis-tribution, which validates the theory.

Tanguy Le BorgneUniversity of Rennes, Francetanguy.le-borgne@univ-rennes1.fr

Magnetic Resonance Measurement of TransportDynamics and Mixing in Biogeochemical Precipi-tation

Geoengineering the subsurface to sequester carbon diox-ide is a current topic of societal and technological interest.Significant theoretical advances in modeling and simula-tion of reactive transport processes in porous media haveoccurred recently. Noninvasive magnetic resonance (MR)measurement of the water phase molecular displacementlength and time scale dependent dynamics due to hydro-dynamic dispersion in porous media characterize transportand mixing. The use of MR data in testing and analyzingreactive transport models is considered.

Joseph D. SeymourUnivesity of Montanajseymour@coe.montana.edu

Anomalous Kinetics of Reactive Fronts in PorousMedia

The dynamics of reactive transport phenomena in porousmedia derive from the interaction of microscopic masstransfer and reaction processes. The understanding of ob-served reaction behavior requires the quantification of thesemicroscale processes and their impact on the large scale re-action and transport behavior. Here we study the mixinglimited (fast) reaction A + B –¿ C at the pore-scale, andits effective behavior on the mesoscale, as a paradigmaticcase that allow us to provide a connection between localmixing properties and global reaction kinetics

Pietro de AnnaMIT, Boston, USApietro.deanna@gmail.com

Domain Decomposition forPoroelasticity-Elasticity Systems

A domain decomposition framework is discussed, which isapplicable for large systems that dynamically couple poroe-lasticity and elasticity. Mortar finite elements are used toimpose physically meaningful interface conditions.

Benjamin GanisThe University of Texas at AustinCenter for Subsurface Modelingbganis@ices.utexas.edu

Darcy vs Brinkman

Different laws for describing filtration of a fluid through aporous medium can be found in the literature. We focuson Darcy’s law and Brinkman’s law. They have differentmathematical structure, but they can both be derived fromthe Navier-Stokes system using homogenization in periodicmodel of porous medium, depending on the magnitude ofpermeability.

Eduard Marusic-PalokaDepartment of Mathematics,University of Zagreb, Croatiaemarusic@math.hr

Full Finite Volume Discretization for Poroelasticity

The standard approach to discretization of coupled flowand mechanics in geological porous media is to apply fi-nite volume methods to the Darcy flow equation and fi-nite element methods to the deformation equations. Wepropose an alternative approach where both flow and de-formation are discretized using finite volume methods. Weconstruct a novel finite volume discretization for linear elas-ticity, and highlight the coupling between the flow and de-formation discretizations. Convergence is established forhomogeneous cases.

Coupling Biot and Navier-Stokes Equations forModelling Fluid-Poroelastic Media Interaction

We focus on a fluid-poroelastic structure interaction prob-lem arising in hemodynamics. The finite element approxi-mation of such a problem is involved because both subprob-lems are indefinite. Thanks to stabilization techniques, weuse the same finite element spaces for all the variables, sim-

144 GS13 Abstracts

plifying the discretization and the enforcement of the cou-pling conditions. To solve the associated linear system wepropose both a monolithic approach and partitioned pro-cedures. We compare all the methods on a test problem.

Santiago BadiaInternational Center for Numerical Methods inEngineeringUniversitat Politecnica de Catalunya, Barcelona, Spainsbadia@cimne.upc.edu

Annalisa QuainiUniversity of Houstonquaini@math.uh.edu

Alfio QuarteroniEcole Pol. Fed. de LausanneAlfio.Quarteroni@epfl.ch

Hierarchical Multiscale Method for Elastic Me-chanical Deformation of Naturally Fractured Rocks

A multiscale finite-element method (MSFEM) is developedfor solving the elliptic mechanics equation for heteroge-neous porous media. Heterogeneity and anisotropy in theelastic properties may be due to the presence of fractures,as well as, geometric complexity of the reservoir architec-ture. The basis functions, coarse-scale operator, and re-construction kernels are described in detail. We show thatrelatively small-scale features can affect the global defor-mation and stress fields quite significantly, e.g., fault acti-vation and large-scale formation instabilities. We analyzethe MSFEM method for naturally fractured systems, bothin terms of the quality of the coarse-scale (upscaled) oper-ator and overall computational efficiency.

Karine LevonyanStanfordlevonyan@stanford.edu

Hybrid Tree-based Approach to Block-structuredAMR for Finite Volume Methods

Block-structured adaptive meshes have a long tradition inthe numerical solution of hyperbolic PDEs. In contrast, thedevelopment of non-overlapping, strictly tree-based AMRmethods has been motivated predominantly by low- andhigh-order finite element discretizations. We present anapproach that uses the p4est octree algorithms to drivethe parallelization of Clawpack-based numerics for conser-vation laws. We will outline differences and similarities tostructured AMR methods and close with presenting pre-liminary numerical studies.

Donna CalhounBoise State University

donnacalhoun@boisestate.edu

Hybrid Tree-Based Approach to Block-StructuredAMR for Finite Volume Methods on the Sphere

Skepticism persists as to whether the use of adaptive meshrefinement (AMR) can improve atmospheric flow simula-tions. Model developers are reluctant to engage in AMRcode development amid concerns that multi-resolutiongrids are ineffective in the absence of precise error esti-mators or can damage numerical solutions. We proposea highly scalable, spatially adaptive code to test modernfinite volume discretizations on Cartesian grids, and es-tablish their effectiveness on several benchmarks in atmo-spheric flows.

Donna CalhounBoise State Universitydonnacalhoun@boisestate.edu

Wavelet-Based Dynamic Adaptivity for theShallow-Water Equations on Staggered Meshes

This talk presents a dynamically adaptive wavelet methodfor the shallow water equations on a staggered hexago-nal C-grid, designed so it can be extended easily to theicosahedral subdivision of the sphere. Distinct biorthog-onal second generation wavelet transforms are developedfor the pressure and the velocity, together with compat-ible restriction operators ensuring mass conservation andno numerical generation of vorticity. The conservation anderror control properties of the method are verified by apply-ing it to a propagating inertia-gravity wave packet and torotating shallow water turbulence. Even in the latter casesignificant savings in the number of degrees of freedom areachieved.

Thomas DubosLMDEcole Polytechniquedubos@lmd.polytechnique.fr

Nicholas KevlahanDepartment of Mathematics & StatisticsMcMaster Universitykevlahan@mcmaster.ca

Imex Methods for Continuous and Discontinu-ous Galerkin Methods for the Compressible EulerEquations: Applications to Nonhydrostatic Atmo-spheric Modeling

We have been developing 3D fully parallel compressibleEuler solvers using high-order continuous (CG) and dis-continuous Galerkin (DG)methods. The focus of thismodel is towards numerical weather prediction at both thelimited-area and global scale. In order to improve the effi-ciency of these models, we construct Implicit-Explicit time-integrators whereby the slow modes (advection) are treatednonlinearly and explicitly while the fast modes (acoustics)

GS13 Abstracts 145

are treated linearly and implicitly. In this talk, I will de-scribe the challenges we have faced in constructing IMEXmethods for both CG and DG methods. For example, inorder to increase the efficiency of the methods requires ex-tracting the Schur Complement of the IMEX system whichis non-trivial for DG methods. I will report on the ideasthat have proven successful and those that have not forboth CG and DG.

Francis X. GiraldoNaval Postgraduate Schoolfxgirald@nps.edu

A Discontinuous Galerkin Scheme for a 2-EquationVertical Eddy Viscosity Parameterization

Vertical eddy viscosity parametrizations are one of the keycomponents of ocean models affecting the model skill andits performance. Here we discuss our implementation of the2-equation generic turbulence length scale parametrization(Umlauf, Burchard, 2003) within UTBEST3D – a 3D dis-continuous Galerkin simulator. A specialty of our approachis the discretization of the turbulence unknowns with thehelp of a 1D discontinuous Galerkin method on verticalsegments.

Vadym AizingerUniversity of Erlangenaizinger@math.fau.de

Adaptive Galerkin Type Methods for InundationComputations

Tsunami as well as storm surge simulation requires accu-rate and robust simulation techniques capable of resolv-ing the large scale features (in deep ocean) and the smallscale phenomena (usually near the shore). This is achievedby using Galerkin-type (finite element and discontinuousGalerkin) numerical approximations on adaptively refinedmeshes. In this presentation we focus our attention to effi-ciency and accuracy of the numerical schemes in inundationapplications.

Green-Naghdi solutions to the Pressure Poissonequation with Boussinesq-type scaling

One of the most challenging aspects of numerically mod-eling near shore wave dynamics is balancing computa-tional cost and accuracy. One approach to reducing cost isthrough Boussinesq–type scaling, however the irrotation-ality assumption is often invalid for near–shore physics. ABoussinesq–type scaling without the assumption of irrota-tionality is presented. Solutions to the Pressure Poissonequation using a Green-Naghdi approach are shown to beadvantageous in terms of cost and order of the solution.

Aaron DonahueUniversity of Notre Dameadonahu1@nd.edu

Joannes WesterinkDepartment of Civil Engineering and Geological Sciences

University of Notre Damejjw@nd.edu

Andrew KennedyUniversity of Notre Dameandrew.b.kennedy.117@nd.edu

Ethan KubatkoThe Ohio State Universityekubatko@gmail.com

From a Geological to a Numerical Model for Earth-quake Generation (and fluids reaction)

We model the state of stress and the circulation of fluidsin faults cross-cutting the brittle-ductile transition (BDT).The fault is assumed have stickslip behavior in the brittlecrust and to deform by steady-state shear in the ductilecrust. These contrasting behaviors determine a stress andstrain gradient at the BDT that is dissipated during theearthquake. Changes in porosity and permeability at theBDT from interseismic to coseismic stages control fluid dis-charge.

Eugenio CarminatiDept. of Earth Sciences, Universita la SapienzaRome, Italyeugenio.carminati@uniroma1.it

Carlo DoglioniUniversita La Sapienzacarlo.doglioni@uniroma1.it

Salvatore Barba, Federica RiguzziIstituto Nazionale di Geofisica e Vulcanologia, Rome,Italysalvatore.barba@ingv.it, federica.riguzzi@ingv.it

Surface Water Enables Subduction on Earth: Pre-dictions from Self-Consistent Models

Fully coupled solid-fluid numerical models demonstratethat the presence of surface water controls both initia-tion and style of subduction via local brittle/plastic rockstrength reduction. Although subduction fails to initiateunder fluid-absent conditions, it can naturally start andbecome self-sustaining when porous water is present in-side oceanic crust and along the plate boundaries. Fluidpercolation localizes along spontaneously forming fractureswhere high fluid pressure compensates lithostatic pressure,thus dramatically decreasing friction along the subductionzone.

Taras GeryaGeophysical InstituteETH-Zurichtaras.gerya@erdw.ethz.ch

Consequences of Viscous Anisotropy in Partially

146 GS13 Abstracts

Molten Rocks

In partially molten regions of Earth, rock and magma co-exist as a two-phase aggregate in which the solid grains ofrock form a viscously deformable matrix. Liquid magmaresides within the permeable network of pores betweengrains. Deviatoric stress causes the distribution of con-tact area between solid grains to become anisotropic; thiscauses anisotropy of the matrix viscosity. The anisotropicviscosity tensor couples shear and volumetric componentsof stress/strain rate. This coupling, acting over a gradientin shear stress, causes segregation of liquid and solid. Liq-uid typically migrates toward higher shear stress, but underspecific conditions, the opposite can occur. Furthermore,in a two-phase aggregate with a porosity-weakening vis-cosity, matrix shear causes porosity perturbations to growinto a banded structure. We show that viscous anisotropyreduces the angle between these emergent high-porosityfeatures and the shear plane. This is consistent with labexperiments.

Richard F. KatzUniversity of OxfordRichard.Katz@earth.ox.ac.uk

Yasuko TakeiEarthquake Research InstituteUniversity of Tokyoytakei@eri.u-tokyo.ac.jp

Improved Rheological Models for the Descriptionof Rift Dynamics

Oceanic rift processes are due to diverget plate tectonics,these zones represent the fundamental areas where to inves-tigate lithosphere/mantle interactions. The developmentof a mathematical model is required in order to exploitmodern numerical tools to give a detailed description ofthe structures developed in rift areas. In this talk a setof novel mathematical models (in accordance with mod-ern geological observations) to describe the rift processesis presented.

Marco CuffaroIstituto di Geolgia Ambientale e Geoingegneria (IGAG)Consiglio Nazionale delle Ricerche (CNR)marco.cuffaro@igag.cnr.it

Edie MiglioPolitecnico di Milano (Italy)MOX, Dept. of Mathematicsedie.miglio@polimi.it

Mattia Penati, Marco ViganMOX, Dept. of Mathematics, Politecnico di MilanoMilano, Italymattia.penati@gmail.com, marco.viga@gmail.com

Wgfem for Elliptic Interface Problems

Lin MuMichigan State Universitylxmu@ualr.edu

Knut WaaganUniversity of Washingtonkwaagan@uw.edu

Weak Galerkin Finite Element Methods for EllipticProblems

Junping WangNational Science Foundationjwang@nsf.gov

Wgfem for Biharmonic Problems

Xiu YeUniversity of Arkansas, Little Rockxxye@ualr.edu

Bayesian Uncertainty Quantification of SubsurfaceFlow Models Using Nested Sampling and SparsePolynomial Chaos Surrogate

An accelerated Bayesian uncertainty quantification methodbased on the nested sampling (NS) algorithm andnon-intrusive stochastic collocation method is presented.Nested sampling is an efficient Bayesian sampling algo-rithm that builds a discrete representation of the posteriordistributions by iteratively re-focusing a set of samples tohigh likelihood regions. The main difficulty of the nestedsampling algorithm is in a constrained sampling step whichis commonly performed using a random walk Markov chainMonte-Carlo (MCMC) algorithm. In the current work, weutilize a two-stage MCMC sampling using a polynomialchaos response surface to filter out rejected samples in theMarkov chain Monte-Carlo method. The combined use ofthe nested sampling algorithm and the two-stage MCMCprovides significate computational gains in terms of thenumber of simulation runs. The proposed algorithm is ap-plied for calibration and model selection of subsurface flowmodels.

Ahmed H. ElSheikhCenter for Subsurface Modeling, ICESUniversity of Texas at Austin, TX, USAaelsheikh@ices.utexas.edu

Mary F. WheelerCenter for Subsurface Modeling, ICESUniversity of Texas at Austinmfw@ices.utexas.edu

Ibrahim HoteitKing Abdullah University of Science and Technology(KAUST)ibrahim.hoteit@kaust.edu.sa

GS13 Abstracts 147

Toward An Expectation-Maximization Method forParameter Estimation and Its Application to RateEstimation in Oil Wells

Information of flow rates in individual wells is crucialfor production optimization and reservoir management.To obtain this information, a framework has been devel-oped consisting of a transient wellflow model, a stochas-tic flowrate model, and estimation methods. The stochas-tic flowrate model used in the framework needs to specifythe variances of the driving noise terms. In this talk, anExpectation-Maximization (EM) based method is adoptedto automatically estimate these parameters in an onlinefashion.

Xiaodong Luo

International Research Institute Of Stavanger (IRIS)xiaodong.luo@iris.no

Rolf Johan Lorentzen, Andreas Stordal, Geir NaevdalInternational Research Institute Of Stavanger (IRIS)Bergen 5008, Norwayrolf.lorentzen@iris.no, andreas.stordal@iris.no,geir.naeval@iris.no

Multiple Criteria Optimization of CO2 Sequestra-tion Strategy Under Geological Uncertainty UsingAdaptive Sparse Grid Surrogates

The key to successful CO2 sequestration depends on eco-nomic efficiency, capacity and long-term security of CO2

storage. Making decisions in injection strategies undermultiple objectives become a challenging task due to ge-ological uncertainty and conflicting objectives. In the cur-rent work, we used Non-dominated Sorting Genetic Algo-rithm (NSGA-II) based on Adaptive Sparse Grid Interpo-lation (ASPI) to maximize sweep efficiency, economic cri-teria, and simultaneously minimize risks associated to CO2

injection. Numerical results showed that a Pareto-optimalfront of the injection strategies is essential to making adecision in CO2 sequestration projects.

Rachares PetvipusitQCCSRC, Department of Earth Science and EngineeringImperial College Londonrp11@imperial.ac.uk

Martin BluntDept. Earth Science and EngineeringImperial College Londonm.blunt@imperial.ac.uk

Peter KingImperial College LondonDepartment of Earth Science & Engineeringpeter.king@imperial.ac.uk

Multilevel Monte Carlo for Groundwater Flow

Problems in Random Media

Partial differential equations (PDEs) with random coeffi-cients are used in computer simulations of physical pro-cesses in science, engineering and industry applicationswith uncertain data. The goal is to obtain quantitativestatements on the effect of input data uncertainties for acomprehensive evaluation of simulation results. However,these equations are formulated in a physical domain cou-pled with a sample space generated by random parametersand are thus very computing-intensive. We outline thekey computational challenges by discussing a model ellipticPDE of single phase subsurface flow in random media de-scribed by correlated lognormal distributions. In this appli-cation the coefficients are often rough, highly variable andrequire a large number of random parameters which putsa limit on all existing discretisation methods. To overcomethese limits we employ multilevel Monte Carlo (MLMC),a novel variance reduction technique which uses samplescomputed on a hierarchy of physical grids. A rigorous con-vergence and complexity analysis of MLMC requires theestimation of the error introduced by the finite elementdiscretisation. We extend recent works on the analysis ofstandard nodal finite elements to mass-conservative low-est order Raviart-Thomas mixed finite elements. This isvery important since the use of mass-conservative discreti-sation schemes is highly desirable in realistic groundwaterflow problems. As in the standard case, the analysis isnon-trivial due to the limited spatial regularity and theunboundedness of the employed lognormal random fields.This is joint work with Andrew Cliffe (Uni Nottingham),Mike Giles (Uni Oxford), Ivan Graham (Uni Bath), MinhoPark (Uni Nottingham), Robert Scheichl (Uni Bath) andAretha Teckentrup (Uni Bath).

Elisabeth UllmannUniversity of BathE.Ullmann@bath.ac.uk

An Adaptive Fast Multipole Accelerated BoundaryElement Method for 3D Elastodynamics

The Boundary Element Method is well suited to the com-putation of elastic wave propagation as only the domainboundaries are discretized. This advantage is offset bythe fully-populated matrix. Considerable speedup of so-lution time and decrease of memory requirements areachieved with the Fast Multipole Method. This speedsup the matrix-vector product computation at each itera-tion. Then, additional gains in CPU time and accuracyare reached by using a dedicated mesh adaptation proce-dure.

Stephanie ChaillatPOems-ENSTAstephanie.chaillat@ensta-paristech.fr

Adrien LoseilleINRIA Paris-Rocquencourtadrien.loseille@inria.fr

Up-scaling 3D Complex Geological Media for theElastic Wave Equation

Seismic waves propagating in the Earth are affected bydifferent sizes of heterogeneities. When modelling thesewaves, taking into account small heterogeneities is a chal-

148 GS13 Abstracts

lenge because it often requires important meshing effortsand leads to high numerical costs. In the recent years,this problem has been overcome by applying the homoge-nization technique (originally developed in solid mechanicsfor periodic media) to the elastic wave equation in non-periodic media (Capdeville et al 2010a,b; Guillot et al2010). This technique allows to upscale the small het-erogeneities and yields a smooth effective medium and ef-fective equations. In this presentation we first recall thetheory of the homogenization, then we describe its imple-mentation in the 3D case, and we finally show applicationswhich validate our code.

Paul CupillardIPG Parispaul.cupillard@univ-lorraine.fr

Yann CapdevilleCNRSyann.capdeville@univ-nantes.fr

Forward and Inverse Problems in Acoustics andSeismic Modeling: An Optimized-Spectral Ele-ment Approach

Spectral-element methods for adjoint/inverse problemshave evolved significantly in recent years. We will dis-cuss recent improvements that have been implemented inthe SPECFEM3D package, namely coupling with a re-gional quasi-analytical solution, wavelet compression, andsource encoding. We will also show a real applicationto seismological data obtained in the Pyrenees region inSouthern France in the context of the ANR PYROPE /TOPOIBERIA transportable recording array experimentthat has been carried out in recent years.

Dimitri KomatitschCNRS Research Director (DR CNRS)komatitsch@lma.cnrs-mrs.fr

Zhinan XieCNRS & Universite de Marseillexiezhinan@lma.cnrs-mrs.fr

Dicontinuous Galerkin Approximation of SeismicWave Propagation Problems

In this talk we present SPEED-SPectral Elements in Elas-todynamics with Discontinuous Galerkin- a high perfor-mance open-source numerical code for seismic wave prop-agation problems. Based on the Discontinuous Galerkinparadigm, allows the treatment of non-uniform polynomialdegree distribution as well as a locally varying mesh size.We show validation benchmarks that demonstrate the ac-curacy, stability, and performance of the parallel kernel aswell as applications of SPEED for simulating realistic mul-tiscale wave propagation phenomena.

Ilario Mazzieri, Paola F. AntoniettiPolitecnico di Milanoilario.mazzieri@mail.polimi.it, paola.antonietti@polimi.it

Alfio QuarteroniEcole Pol. Fed. de LausanneAlfio.Quarteroni@epfl.ch

An Efficient Numerical Approach for ReactiveMultiphase Multicomponent Flow in Porous Me-dia

We present an efficient numerical model for the simulationof partially miscible two-phase multicomponent flow withchemical reactions. The choice of primary variables is suit-able to deal with phase transitions which are handled by acomplementarity approach. A model-preserving reformu-lation technique is applied to eliminate unknowns and theremaining system is solved by a global-implicit approachusing Newton’s method.

Fabian BrunnerUniversity of Erlangenbrunner@math.fau.de

Peter KnabnerDepartment of MathematicsUniversity of Erlangenknabner@math.fau.de

Efficient Numerical Simulation of 2D and 3D Mul-ticomponent Reactive Transport

We present complex scenarios of multicomponent reactivetransport in 2-D and in 3-D. These scenarios are furtherdevelopments of the setting given by the MoMaS bench-mark. We show how to solve the equations using a globalimplicit approach in an efficient way, and we present thederived computational results.

Serge Krautle, Alexander VibeDepartment of MathematicsUniversity of Erlangen-Nuremberg, Germanykraeutle@am.uni-erlangen.de, vibe@am.uni-erlangen.de

Joachim HoffmannUniversity of Erlangen-NurembergDepartment of Mathematicshoffmann@am.uni-erlangen.de

Peter KnabnerFriedrich-Alexander University Erlangen-Nurenberg,GermanyDepartment of Mathematicsknabner@am.uni-erlangen.de

Importance of Non-Negative Numerical Solutionfor Mixing-Controlled Reactive Transport

Conventional numerical methods for reactive transport canproduce non-physical values, particularly for heterogeneousflow fields, irregular grids and full tensor dispersion. Nega-tive concentrations cannot be tolerated for nonlinear reac-tions. We present several computational strategies to ad-dress these issues for mixing-controlled reactions. The fluxcorrected transport framework is a flexible method thatcan be used with existing simulators. We also present aFEM formulation that uses optimization to strictly enforcemaximum principles and the non-negative constraint.

Albert J. ValocchiUniversity of Illinois at Urbana-Champaignvalocchi@illinois.edu

GS13 Abstracts 149

Kalya NakshatralaDepartment of Civil and Environmental EngineeringUniversity of Houstonknakshat@central.uh.edu

Isotopic Management in the Reactive TransportCode Hytec : Isotopic Fractionation and Radioac-tive Decay

HYTEC is a coupled reactive transport code used for awide variety of applications in geosciences. This workpresents a new functionality : the isotopic management.This new option allows to take into account any even com-plex radioactive decay chains and chemical isotopic frac-tionation at equilibrium. The effective implementation ofthe new option is presented as well as two illustrative ex-amples with comparison to analytical solutions: one for theradioactive decay, and the other for isotopic fractionation.

Caroline de Dieuleveult, Vincent LagneauGeosciences CenterMINES ParisTechcaroline.de dieuleveult@mines-paristech.fr,vincent.lagneau@mines-paristech.fr

Autofocusing of Internal Multiples and Applicationto Multidimensional Deconvolution

We describe a method that reconstructs the wavefield froma virtual source inside a medium without needing a re-ceiver at the virtual-source location. An estimate of thedirect arriving wavefront is required in addition to reflec-tion data. This method allows us to decompose the re-constructed wavefield in up- and down-going components.We illustrate the method with numerical examples in loss-less acoustic media. This method is a basis for techniquesrelying on Multi Dimensional Deconvolution.

Filippo Broggini, Roel SniederColorado School of Minesfbroggin@mines.edu, rsnieder@mines.edu

Kees WapenaarDepartment of Geoscience and EngineeringDelft University of Technologyc.p.a.wapenaar@tudelft.nl

Joost van der NeutCITG, Delft University of Technologyj.r.vanderneut@tudelft.nl

Wavefield Tomography Based on Local Image Cor-relations

A smooth model of the subsurface is necessary to mapwaves recorded at the surface where contrasts in physi-cal parameters exist. The model is unknown and must beestimated from the data. Contrast interfaces are describedby position and orientation. If the model is accurate, thereflector positions are invariant with respect to an exten-sion parameter (e.g., shot index). Our inversion procedureis based on similarity of the reflector orientations and re-quires fewer images.

Francesco Perrone

Center for Wave PhenomenaColorado School of Minesfperrone@mines.edu

Paul C. SavaColorado School of Minespsava@mines.edu

Renormalization of Scattering Series and the Im-provement of Convergence Property

It is well known that the forward or inverse Born scatteringseries is of the Fredholm type and its convergence is limitedto a region of weak scattering regime. The current statusin application of the higher order Born series is to calculateonly a few terms and see the improvement compared withthe first order term. In this work, we apply the De Wolf se-ries method (De Wolf transform) to reorder and renormal-ize the Born series, and hence transform the Fredholm typeinto a Volterra-type series which has a guaranteed conver-gence. Numerical examples are given to demonstrate theconvergence and efficiency of the De Wolf approximationfor multiple forward-scattering.

Ru-Shan WuUniversity of California, Santa Cruzrwu@ucsc.edu

Lingling YeUniv of California, Santa Cruzlye2@ucsc.edu

Interferometric Imaging of the Leading-order In-ternal Multiples

We develop a three step imaging procedure, which wouldimage the first order internal scattering. This approachmainly utilizes the background Green’s function from thesurface to each image point. We first back propagate of therecorded surface data using the background Green’s func-tion down to the image point. Next, we cross-correlate theback-propagated data with the recorded surface data. Fi-nally, we cross-correlate the result of second step with thebackground Green’s function form surface to image point.This would give us the image of the point from which sin-gle scattering has not been recorded. Note that this inter-nal multiple imaging procedure will image only the pointswhich has taken part in a single order internal scatteringand single scattering points will be suppressed. We addthis image to those obtained from any of the many singlescattering based imaging procedure, for example, Kirchhoffmigration, to give the total image. Application to syntheticdata with reflectors illuminated by multiple scattering onlydemonstrates the effectiveness of the approach. We shallalso show that the first order internal scattering is imagedby the conventional Reverse Time Migration (RTM), butis very weak compared to single scattering image and causepossible crosstalk. In our method, by cross-correlating theback propagated field with the data we manage to sepa-rate the second order term in the Born scattering series(first order internal scattering), which enhances the imagecorresponding to that term.

Mohammad A. ZuberiKAUSTmohammad.zuberi@kaust.edu.sa

150 GS13 Abstracts

Tariq AlkhalifahKing Abdullah University of Science and Technologytariq.alkhalifah@kaust.edu.sa

A Numerical Study of Splitting Schemes and Im-plicit Solution Methods for Biot’s Equation

The stability of splitting schemes for Biot’s equation hasrecently been studied by Mikelic and Wheeler [1], and oth-ers. We will investigate the performance of these stablesplittings, and compare them with a fully implicit solu-tion method on two cases which are numerically difficult.We will also look at a reformulation of the most promisingsplitting scheme as a block preconditioner for a fully im-plicit solver. [1] A. Mikelic, M. F. Wheeler: Convergence

of iterative coupling for coupled flow and geomechanics,Computational Geosciences, 2012. DOI: 10.1007/s10596-012-9318-y

Joachim B. Haga, Kent MardalSimula Research Laboratoryjobh@simula.no, kent-and@simula.no

Eirik KeilegavlenUniversity of BergenEirik.Keilegavlen@uib.no

Inexact Linear Solvers for Control Volume Dis-cretizations

We discuss the construction of inexact linear solvers forcontrol volume discretizations of elliptic problems. Themethods are formulated as multi-level discretizations whichpreserve the conservation structure of the continuous prob-lem, and conservative flux fields are produced even forinexact pressure solutions. Thus the linear solver allowsfor significant computational savings while still producingphysically meaningful solutions. The iterations are con-trolled by error estimates. Numerical experiments verifythe viability of our approach.

Eirik Keilegavlen, Jan M. NordbottenUniversity of BergenEirik.Keilegavlen@uib.no, jan.nordbotten@math.uib.no

Multiscale Methods: Tools to Balance Accuracyand Efficiency

In the description of flow through porous media, approx-imate solution based on upscaling procedures have beenwidely employed. Recent advances in adaptive multiscaletechniques offer a general framework that enables greatflexibility in balancing accuracy and efficiency. However,an optimal choice is possible only if the objectives areclearly defined and the particular application specified. Wediscuss this topics in relation to the MsFV method.

Ivan Lunati, Laureline Josset, Rouven KuenzeUniversity of Lausanneivan.lunati@unil.ch, laureline.josset@unil.ch,

rouven.kunze@unil.ch

A Posteriori Error Estimates, Stopping Criteria,and Adaptivity for Two-Phase Flows

We show how computable a posteriori error estimates canbe obtained for the two-phase porous media flow problem.Iterative linearizations by, e.g., the Newton method anditerative solutions of the arising linear systems are typi-cally involved in the numerical approximation procedure.We show how the corresponding error components can bedistinguished and estimated separately. A fully adaptivesolution procedure, with adaptive choices of the number ofnonlinear and linear solver steps, the time step size, andthe computational mesh, is presented.

Martin VohralikUniversite Pierre et Marie CurieParis, Francemartin.vohralik@inria.fr

Clement CancesUniversity Paris VILaboratoire J.L. Lionscances@ann.jussieu.fr

Sorin PopCASAEindhoven University of Technologyi.pop@tue.nl

A Multilevel Time Integrator for Large-scale At-mospheric Flows

We present a numerical scheme aimed at simulating mul-tiscale atmospheric flows in the low Mach number regime.Compressible flow equations are discretized with a second-order accurate projection method. Results obtained withthe advection of a vortex, an acoustic wave and a ris-ing warm air bubble showcase the method’s performance.With a multilevel time integration approach based onmultigrid ideas, the scheme can handle multiscale featuresaround balanced regimes in a controlled fashion.

Tommaso BenacchioFreie Universitaet Berlinbenacchio@math.fu-berlin.de

Rupert KleinFreie Universitat Berlinrupert.klein@math.fu-berlin.de

Exponential Integrators for Applications to Envi-ronmental Fluid Dynamics

The accuracy and performance of some kinds of exponen-tial time integrators are assessed for the time discretizationof hyperbolic problems. In particular, their potential forapplications to environmental fluid dynamics problems isassessed by comparison with more common time discretiza-

GS13 Abstracts 151

tion techniques. Possible extensions of the standard expo-nential methods discussed in the ODE literature will alsobe discussed.

Luca BonaventuraMOX Politecnico di MilanoMilan, Italy 20133luca.bonaventura@polimi.it

Comparison of Adaptive and Uniform DG Simula-tions

Adaptive mesh refinement generally serves to increase com-putational efficiency without compromising the accuracy ofthe numerical solution significantly. However it is an openquestion in which regions the spatial resolution can actuallybe coarsened without affecting the accuracy of the resultsignificantly. This question is investigated for the simula-tion of warm air bubble test cases. For this purpose a novelnumerical model is developed that is tailored towards thisspecific meteorological problem. A method is introducedwhich allows one to compare the accuracy between differ-ent choices of refinement regions. For a rising warm airbubble the additional error by using adaptivity is smallerthan 1% of the total numerical error if the average numberof elements used for the adaptive simulation is about 50%smaller than the number used for the simulation with theuniform fine-resolution grid.

Andreas MuellerInstitute for Atmospheric PhysicsMainz Universityamueller@anmr.de

Multiresolution Ocean Simulations with Fesom

Unstructured meshes offer geometric flexibility. In the con-text of large-scale ocean modeling they enable simulationswith a regional focus in an otherwise global setup. TheFinite-Element Sea ice-Ocean circulation Model (FESOM)offers such functionality. A brief review of current FESOM-assisted research will be given, to illustrate the utility of theapproach. New developments include a global cell-vertexfinite-volume setup which is compared to FESOM in globalocean simulations.

Sergey DanilovAlfred Wegener Institutesergey.danilov@awi.de

Local Timestepping in the Discontinuous GalerkinMethod for Shallow Water Systems

Coastal models discretized explicitly in time on unstruc-tured meshes can give rise to severe global CFL timestepconstraints. This constraint is in fact local, depending onthe local eigenvalues of the system and the element meshsize. By allowing the timesteps to vary spatially, one cansignificantly improve computational efficiency. In this talk,we describe a parallel local timestepping approach whichconserves mass and has been observed to be second orderaccurate. Applications to storm surge modeling will bepresented.

Clint DawsonInstitute for Computational Engineering and Sciences

University of Texas at Austinclint@ices.utexas.edu

Corey TrahanDRCVicksburg, MS USAtrahancj@gmail.com

Pressure Forcing and Dispersion Analysis for Dis-continuous Galerkin Approximations to OceanicFluid Flows

This work is part of an effort to study the potential applica-tion of DG methods to the numerical modeling of the gen-eral circulation of the ocean. One step performed here is todevelop an integral weak formulation of the pressure forc-ing that is suitable for usage with a DG method and with ageneralized vertical coordinate that includes level, terrain-fitted, and isopycnic coordinates as examples. This formu-lation is then tested, in special cases, with some compu-tational experiments and with analyses of well-balancing,dispersion relations, and numerical stability.

Robert L. HigdonOregon State Universityhigdon@math.oregonstate.edu

Adaptive Vertical Coordinates for Modeling Strat-ified, Coastal Seas

An adaptive strategy for the vertical gridding in terrain-following 3D ocean models is presented here, which is de-signed for reducing discretisation errors in ocean models.With this, internal flow structures such as pycnoclines canbe well resolved and followed by the grid. A set of exam-ples is presented, which show that the adaptive grid strat-egy reduces pressure gradient errors and numerical mixingsignificantly and improves the representation of physicalprocesses, nutrient fluxes and plankton growth.

Richard HofmeisterHelmholtz-Zentrum Geesthachtrichard.hofmeister@hzg.de

Jean-Marie BeckersUniversity of Liege, MARE-GHER-AGO, Belgiumjm.beckers@ulg.ac.be

Ulf GraweLeibniz Institut for Baltic Sea Research, Warnem{Germanyulf.graewe@io-warnemuende.de

Hans BurchardLeibniz Institut for Baltic Sea Research, Warnemunde,Germanyhans.burchard@io-warnemuende.de

Aspect: An Advanced Solver for Problems in EarthConvection

Simulating convection in Earth’s mantle is challenging formany reasons: the vastly varying scales, nonlinear materialbehavior, advection dominated transport, and long timespans of interest. We present an overview of the open

152 GS13 Abstracts

source code ASPECT that uses modern numerical meth-ods for adaptive mesh refinement, solvers and stabilizationto solve convection problems in Earth. It is written witha particular focus on extensibility and scales to very largecomputations.

Wolfgang BangerthTexas A&M Universitybangerth@math.tamu.edu

Timo HeisterTexas A&M UniversityDepartment of Mathematicsheister@math.tamu.edu

Flexible Finite Element Methods for Geodynamics

The FEniCS Project is an open source solution for theautomated solution of differential equations and is largelydeveloped at Simula. Recently, we have applied FEniCS tomantle convection problems and tested it against publishedbenchmarks. FEniCS as a generic solver can complementexisting purpose built software for rapid deployment, com-plex and adaptive meshes and adjoint problems.

Stuart R. Clark, Lyudmyla VynnytskaSimula Research Laboratorystuart@simula.no, lyudav@simula.no

Improved Thermo-Tectonic Basin Reconstructionwith P-T Dependent Gravimetric Calibration

Source rock maturity depends on the thermal evolutionof sedimentary basins. Modeling this requires a tectonicmodel that resolves the basin and the lithospheric scale.Unfortunately, no unique solution exists. This can be im-proved by including datasets usually not considered in thebasin-modeling context. Here we show that calibrationwith the gravity signal leads to better-constrained thermo-tectonic basin models. This approach also improves grav-ity modeling, as the thermal state of the lithosphere canbe included.

Dani SchmidGeomodelling Solutions GmbhZurich, Switzerlanddani.schmid@geomodsol.com

Lars RuepkeGeoModelling Solutions GmbHlars.ruepke@geomodsol.com

Matilde Dalla Rosa, Matteo GilardiENI S.p.A.matilde.dalla.rosa@eni.com, matteo.gilardi@eni.com

Simulating Mantle Convection, Plate Tectonics andthe Thermo-Chemical Evolution of Planetary Inte-riors in a 3-D Spherical Shell on High-PerformanceComputers

It is now possible to perform global 3D spherical modelsof solid Earth evolution that span 4.5 billion years, includeself- consistently generated plate tectonics and magmatismthat produces crust and chemically differentiates the man-

tle. Such calculations make predictions that can be com-pared to observations from seismology, geochemistry, pale-omagnetism and geology. We are also applying such modelsto other planets, both in our own solar system and aroundother stars (super-Earths).

Paul TackleyDepartment of Earth SciencesETH Zurich Institute fuer Geophysikpaul.tackley@erdw.ethz.ch

Methods to Determine the Effective Resolution ofDynamical Cores

The effective resolution of a model is the smallest scalethat is fully resolved. We present theoretical methods andidealized test cases to determine the effective resolution ofdynamical cores. Investigating the dissipative and disper-sive properties of a scheme determines which wavenumbersare resolved for linear systems. Using baroclinic wave tests,we can numerically determine which scales are resolved forthe nonlinear system. We present results for NCAR’s Com-munity Atmosphere Model finite-volume core.

James KentUniversity of Michiganjdkent@umich.edu

Adaptive Mesh Re-finement for the Non-Hydrostatic Unified Modelof the Atmosphere (NUMA)

The Adaptive Mesh Refinement algorithm was designed forthe Discontinuous Galerkin (DG) method in frame of a 2Dmesoscale version of the Non-hydrostatic Unified Model ofthe Atmosphere. An investigation of the algorithm andits interaction with IMEX time-stepping was performed.The implementation was extended to include the Contin-uous Galerkin (CG) method formulation. We present thebehavior of both DG and CG methods for non-conformingadaptive simulations on a suite of test cases employing bothstatically and dynamically refined grids.

Michal A. Kopera, Francis X. GiraldoNaval Postgraduate Schoolmakopera@nps.edu, fxgirald@nps.edu

The Endgame Dynamical Core: Test Results Usinga Switchable Discretisation

ENDGame is the next dynamical core for the Met Office’sUnified Model to be used for weather and climate predic-tion across a range of time and space scales. ENDGameemploys a flexible discretisation of the deep atmospherenonhydrostatic equations allowing a number of simplifica-tions to be made. The effects of a number of these for-mulation switches in ENDGame are investigated using avariety of idealised tests - results and the lessons learntwill be discussed.

Thomas MelvinMet Officethomas.melvin@metoffice.gov.uk

GS13 Abstracts 153

Potential Vorticity Anomalies: Dynamic Or Nu-merical Artifact?

Conservation breaking anomalies in the dynamic potentialvorticity (PV) field have been observed in simulations formodels as simple as the Eady model. These anomalies oc-cur when isentropic (constant potential temperature) sur-faces intersect the surface (in the case of the atmosphere).We make use of a dry baroclinic wave test case to investi-gate this phenomenon, and consider whether it is desirablefor a dynamical core to capture these anomalies, and theconsequences of these features on the other pertinent dy-namical fields.

Jared WhiteheadLos Alamos National Laboratorywhitehead@lanl.gov

Well Placement Optimization Using StochasticApproximated-Gradient Methods

Stochastic approximated-gradient methods combine theadvantages of both gradient-based and stochastic optimiza-tion algorithms without the corresponding computation ef-fort. Two algorithms, EnOpt and FSP, are investigatedand compared for well placement optimization in this work.They do not require access to simulator code and generally,the gradient approximation is independent of the problemdimensions. The results indicate that FSP tends to showimproved convergence characteristics and requires a lessercomputational effort in comparison to EnOpt.

Yuqing Chang, Deepak DevegowdaMewbourne School of Petroleum and GeologicalEngineeringUniversity of Oklahomayuqing.chang@ou.edu, deepak.devegowda@ou.edu

Dual Ensemble Filtering for States Estimation ofCoupled Subsurface Transport Models

Modeling contaminant evolution in geologic aquifers re-quires coupling a groundwater flow model with a contami-nant transport model. This coupling may provide accuratefuture estimates of the subsurface hydrologic state if as-sisted with essential flow and contaminant data throughdata assimilation. Assuming perfect flow, an ensembleKalman filter (EnKF) can be directly used for data assim-ilation into the transport model. This is; however, a crudeassumption as flow models can be subject to many sourcesof uncertainties. If the flow is not accurately simulated,contaminant predictions will likely be inaccurate even af-ter successive Kalman updates of the contaminant withthe data. The problem is usually better handled when bothflow and contaminant states are concurrently estimated us-ing the traditional joint state augmentation approach. Weintroduce, here, an efficient dual strategy for data assimila-tion into this one-way coupled system by treating the flowand the contaminant models separately while intertwininga pair of distinct EnKFs; one on each model.

Mohamad El-GharamtiKAUST, Saudi Arabiamohamad.elgharamti@kaust.edu.sa

Ibrahim Hoteit

King Abdullah University of Science and Technology(KAUST)ibrahim.hoteit@kaust.edu.sa

Iterative Smoothers for Subsurface Reservoir FlowHistory Matching

On Iterative Smoothers for Bayesian Estimation By: An-dreas S. Stordal Abstract: Approximate solutions forBayesian estimation in large scale models is a topic un-der investigation in many scientific communities with thamain focus being on ensemble based methods such as theensemble Kalman filter or Gaussian mixture filters. Wedefine an iterative smoother version of the adaptive Gaus-sian mixture filter as a robust alternative to adaptive im-portance sampling. The filter is compared to other iter-ative smoothers from a practical and theoretical point ofview. Asymptotic properties of the new smoother are com-puted and compared with a theoretical result on random-ized maximum likelihood. We show that we have asymp-totic optimality under certain conditions, contrary to othersmoothers where the sample distribution depend on thenonlinearity and scaling of the model. The new smoother isalso shown to outperform existing methods on simple prob-lems as well as a one dimensional highly nonlinear reservoirproblem.

Andreas StordalInternational Research Instititue of Stavanger (IRIS)andreas.s.stordal@iris.no

Combining Multidimensional Scaling (MDS) withEnsemble-Based Algorithms for Automatic HistoryMatching

The ensemble Kalman filtering fails to preserve non-Gaussian features of geological facies where there is astrong contrast in permeability values of channels and non-channels locations. We develop a methodology to combinemultidimensional scaling and the ensemble Kalman filterfor updating models for a channelized reservoir. A dis-similarity matrix is computed using the dynamic responsesof ensemble members. This dissimilarity matrix is trans-formed to a lower dimensional space using multidimen-sional scaling. The responses mapped in the lower dimen-sion space are clustered and based on distances between themodels in a cluster and the actual observed response, theclosest models to the observed response are retrieved. Up-dating of models within the closest cluster are performedusing EnKF equations. The results of the update are usedto re-sample new models for the next step.

Reza Tavakoli, Sanjay SrinivasanUT-Austintavakoli@ices.utexas.edu,sanjay.srinivasan@engr.utexas.edu

154 GS13 Abstracts

The Interior-PenaltyDiscontinuous Galerkin Method for Elastic WavePropagation in Fractured Media

Jonas D. De BasabeSeismology DepartmentCICESEjonas@cicese.mx

Mrinal SenInstitute of GeophysicsUniversity of Texasmrinal@ig.utexas.edu

Higher Order Summation-by-parts Methods forSeismic Wave Propagation

A fourth order accurate finite difference method for theelastic wave equation in second order formulation is pre-sented. The numerical method satisfies the principle ofsummation-by-parts (SBP), which guarantees energy sta-bility for arbitrary heterogeneous materials in bounded do-mains, with free surface or Dirichlet boundary conditions.Our approach generalizes to realistic topography by trans-forming the elastic wave equation to curvilinear coordi-nates before it is discretized by the SBP technique.

Anders PeterssonLawrence Livermore National Laboratorypetersson1@llnl.gov

Bjorn SjogreenCenter for Applied Scientific ComputingLawrence Livermore National Laboratorysjogreen2@llnl.gov

Exact Boundary Conditions for Modelling and In-version of Elastic Wave Propagation

Many applications of modelling elastic wave propagationrequire the ability to recompute the wavefield after localmodel alterations. By using so-called exact boundary con-ditions, the computational domain in for instance a finite-difference solution can be arbitrarily truncated and thewavefield recomputed around the region of change. Theupdated wavefield will fully include all high-order long-range interactions between the truncated part and the fullmodel. Applications include full waveform inversion andseismic multiple elimination.

Marlies VasmelETH - Zurichmarlies.vasmel@erdw.ethz.ch

Johan RobertssonETH-Zurichjohan.robertsson@erdw.ethz.ch

Dirk-Jan van ManenSchlumberger Gould Researchdmanen@slb.com

Geological Complexity, Topography and SeismicWave Modelling: Are Finite-Differences Up to theChallenge?

The finite-difference (FD) method is still the most widelyused method for modelling seismic waves in geophysics.However, it is not well-suited for modelling the effect ofthe free-surface, especially in the presence of topogra-phy. Although it is commonly inferred that high-orderfinite-elements (FE) are the only affordable alternative insuch scenarios, we want to show that certain modified FDschemes can satisfy most needs for seismic modelling, in-cluding challenging topographies and geologically complexmodels.

Josep de La PuenteBarcelona Supercomputing CenterSpainjosep.delapuente@bsc.es

Miguel Ferrer, Jose Marıa CelaBarcelona Supercomputing Centermiguel.ferrer@bsc.es, josem.cela@bsc.es

Effective Upscaling of Kinetics in Simulation of in-Situ Combustion Processes

Sustained high oil prices and growing demand have un-locked heavy oil resources. Production of such unconven-tional oils typically requires thermal stimulation. In-situcombustion is an attractive stimulation method as heat isgenerated in the subsurface and the oil can often be up-graded. Performance prediction and optimization of ISCprojects require effective upscaling of reservoir rock proper-ties, fluid properties and kinetics. We propose an effectiveupscaling technique that is competitive in accuracy withtraditional approaches and many times faster.

Margot GerritsenDept of Petroleum EngineeringStanford Universitymargot.gerritsen@stanford.edu

Anna NissenEnergy Resources EngineeringStanford Universityamnissen@stanford.edu

Formulation for Multiphase Multicomponent Flowsand Stopping Criteria for Two-phase Flows

The petroleum industry needs to model multiphase mul-ticomponent flows in large porous domains. These com-putations are very expensive and thus one is interested inoptimizing them. The talk will first discuss a new formula-tion for multiphase multicomponent flow, its finite volumediscretization, and efficient computer implementation. In asecond part, we restrict ourselves to the two-phase settingand present some adaptive stopping criteria for nonlinearand algebraic solvers based on a posteriori error estimates.

GS13 Abstracts 155

Carole Heinry

Universite Pierre et Marie Curie (Paris 6), Paris, Francecarole.heinry@gmail.com

Analysis of Mixed Finite Element Discretization forCrystal Precipitation and Dissolution Model

We deal with the numerical analysis of an upscaled modeldescribing the reactive flow in a porous medium. The so-lutes are transported by advection and diffusion and un-dergo precipitation and dissolution. The reaction term,in particular, the dissolution term has a particular, multi-valued character. We consider the mixed finite elementdiscretization and prove the convergence to the continu-ous formulation. Additionally, this also yields an existenceproof for the model in mixed variational formulation.

Kundan KumarUniversity of Austink.kundan@gmail.com

Florin A. Radu, Florin A. RaduInstitute of MathematicsUniversity of Bergenflorin.radu@math.uib.no, florin.radu@math.uib.no

Locally Mass Conservative Methods with Discon-tinuous Galerkin in Time for Miscible Displace-ment in Porous Media

The miscible displacement problem of a solvent fluid into aresident fluid in porous media is characterized by a systemof coupled partial differential equations. The flow of thefluid mixture is modeled by Darcy’s law, and the concen-tration of the solvent fluid satisfies a transport equation.We propose a high order method in time and space, thatcombines discontinuous Galerkin in time with locally massconservative methods such as mixed finite element meth-ods and interior penalty discontinuous Galerkin methods.Convergence of the numerical solution is obtained undermild regularity assumptions on the data. Boundedness ofthe dispersion-diffusion matrix is not required. The anal-ysis utilizes a generalized Lions-Aubin theorem, that canbe applied to broken Sobolev spaces. Numerical exam-ples show that optimal rates of convergence are reachedfor smooth solutions. Robustness of the method is testedfor heterogeneous porous media.

Beatrice RiviereRice UniversityHouston, Texas, USAriviere@caam.rice.edu

Regularization in Banach Spaces for MicrowaveBorehole Subsurface Prospection

In electromagnetic prospection of buried targets, the elec-tromagnetic scattered field is collected in a set of measure-

ment points located above the air-ground interface or in aborehole arrangement . The relationship between such fieldand the dielectric properties of the targets can be modeledby using a nonlinear integral operator involving the Greenfunction for half-space configurations. In the present work,an algorithm based on regularization in Banach spaces isconsidered to solve the associated inverse scattering equa-tion. With respect to previous algorithms, usually basedon classical Hilbert spaces, the present method in Banachspaces is able to give a substantial reduction of the over-smoothing and ringing effects in the restored buried object.

Claudio EstaticoDepartment of Mathematics, University of Genova, Italyestatico@dima.unige.it

Matteo PastorinoDepartment of Electrical, Electronic, Telecomm. Eng.University of Genoamatteo.pastorino@unige.it

Andrea RandazzoDepartment of Electrical, Electronic, Telecomm. Eng.University of Genoa, Italyandrea.randazzo@unige.it

Lp-Penalized Methods for Spatial Resolution En-hancement of Microwave Radiometer Data

Microwave radiometer data are characterized by a spatialresolution that, although adequate for large-scale phenom-ena, is a severe limitation to observe small-scale features.An effective technique is first proposed to enhance the spa-tial resolution of two-dimensional radiometer data. It isbased on the iterative regularization in Banach Spaces. Itallows reducing the over-smoothing effects and the oscil-lations that are present in standard Hilbert procedures.Experiments undertaken on actual data confirm the effec-tiveness of the approach.

Flavia LentiDepartment of Science and High TechnologyUniversity of Insubria, Como, Italyflavia.lenti@uninsubria.it

Ferdinando Nunziatadepartment of Tecnology, University of NaplesParthenopeferdinado.nunziata@uniparthenope.it

Claudio EstaticoDepartment of Mathematics, University of Genova, Italyestatico@dima.unige.it

Maurizio Migliacciodepartment of Tecnology, University of NaplesParthenopemaurizio.migliaccio@uniparthenope.it

The Cylindrical Wave Approach and the Electro-magnetic Scattering by Buried Objects

The Cylindrical-Wave Approach (CWA) is a spectral-domain method for the full-wave solution of the electro-magnetic forward-scattering problem by subsurface two-

156 GS13 Abstracts

dimensional objects. The scattered field is represented interms of a superposition of cylindrical waves. Use is madeof the plane-wave spectrum to take into account the inter-action of such waves with the interface between air and soil,and between different ground layers. The ground losses andall multiple-reflection and diffraction phenomena are takeninto account.

Fabrizio Frezzafrezza@diet.uniroma1.it

Lara PajewskiRomelara.pajewski@uniroma3.it

Regularized Solution of Linear and NonlinearProblems in Electromagnetic Sounding

Electromagnetic induction techniques are often used fornon-destructive investigation of soil properties, since theyallow to ascertain the presence in the ground of metals,liquid pollutants, or saline water. Maxwell equations leadto a nonlinear model for this problem, which is sometimestransformed into an approximated linear model. In bothcases, the inverse problem is severely ill-conditioned. Wewill introduce the models and present the results of numer-ical experiments on both synthetic and real data.

Giuseppe RodriguezUniversit‘a di Cagliari, Italyrodriguez@unica.it

Caterina FenuUniversity of Cagliari, Italykate.fenu@gmail.com

Lava Flow Simulation with Smoothed Particle Hy-drodynamics on GPU

We present a GPU implementation of the Smoothed Parti-cles Hydrodynamics (SPH) numerical method to solve thedynamic and thermal equations involved in the simulationof lava flows. Our model implements multiple rheologies(newtonian, Bingham, power-law, Hershel-Bulkely), withboth fixed and thermal-dependent parameters, to allowdifferent physical models of liquid lava to be tested; sim-ulations can be run on natural topographies, obtained forexample from an Digital Elevation Model of the locationof the simulated event.

Giuseppe BilottaDMI, UNICTbilotta@dmi.unict.it

Alexis HeraultCNAM, Paris, Francealexis.herault@cnam.fr

Eugenio RusticoINGVCataniaeugenio.rustico@ct.ingv.it

Giovanni RussoUniversity of CataniaDepartment of Mathematics

russo@dmi.unict.it

Ciro Del NegroIstituto Nazionale di Geofisica e Vulcanologiaciro.delnegro@ct.ingv.it

A Discontinuous Galerkin Method for the Simula-tion of Multiphase Pyroclastic Flows

The mixture of gas and solid particles in non-equilibriumconditions that compose a pyroclastic flows is describedwith a set of coupled partial differential equations for themass, momentum and enthalpy of each species. Followingthe methods of lines, a Discontinuous Galerkin space dis-cretization is introduced first, then different explicit timediscretization schemes are adopted. Finally, several exam-ples and comparisons between different numerical schemesare presented.

Susanna CarcanoMOX, Polimisusanna.carcano@gmail.com

Luca BonaventuraMOX Politecnico di MilanoMilan, Italy 20133luca.bonaventura@polimi.it

A Second Order Finite-Difference Ghost-CellMethod for Volcano Deformation Modelling

We propose a novel strategy based on a second order FiniteDifference (FD) ghost-cell method for solving the elasto-static equations in an arbitrary domain described by alevel-set function to compute rock deformation caused bythe pressurization of magma sources. The elasto-staticequations are solved on a regular Cartesian grid and thedomain is defined implicitely by the level-set function. Weconsider two-dimensional cases to validate the method ver-sus analytical solutions and Finite Element results.

Armando CocoDipartimento di Geologia e Geofisica, UNIBAcoco@dmi.unict.it

Gilda CurrentiINGV, Cataniagilda.currenti@ct.ingv.it

Giovanni RussoUniversity of CataniaDepartment of Mathematicsrusso@dmi.unict.it

Ciro Del NegroIstituto Nazionale di Geofisica e Vulcanologiaciro.delnegro@ct.ingv.it

Analysis of Non Equilibrium Effects in the Decom-pression Structure of Multiphase UnderexpandedVolcanic Jets

We have developed a semi-implicit, second-order accuratefinite volume numerical scheme to simulate underexpanded

GS13 Abstracts 157

volcanic jets by means of a N-particle Eulerian multiphaseflow model. We discuss the influence of the grain-size dis-tribution and particle load on the shock wave pattern of su-personic jets issuing from a narrow conduit. The problemof the influence of non-equilibrium phenomena, associatedto the polydisperse nature of the mixture, on the stabilityof the volcanic column is finally addressed.

Tomaso Esposti OngaroINGV, Pisaongaro@pi.ingv.it

Augusto NeriIstituto Nazionale di Geofisica e VulcanologiaSezione di Pisaneri@pi.ingv.it

Simulation of Tropical-Cyclone-Like Vortices inShallow-Water ICON-Hex Using Goal-Oriented R-Adaptivity

We build r-adapted grids to predict the tracks of two in-teracting tropical-cyclone-like vortices. A linear sensitivityanalysis using a finite element model delivers goal-orientederror estimates that indicate each grid cells’ contributionto the error in the cyclone tracks. These estimates are usedto optimize the grid of the hexagonal C-grid shallow-watermodel ICON-hex. Compared to uniform meshes, our ap-proach reduces the required degrees of freedom by a factorof four.

Werner BauerUniversity of HamburgKlimaCampuswerner.bauer@zmaw.de

Mimetic Finite Element Methods forOcean/atmosphere Modelling

We present a finite element framework for the rotating shal-low water equations on the sphere, which could be consid-ered to be an extension of the mimetic C-grid approach of(Ringler, Thuburn, Klemp and Skamarock, 2010) to finiteelement methods. The finite element framework maintainsconservation of potential vorticity and mass, absence ofspurious pressure modes, the capability to preserve energy(although dissipation is required to control oscillations nearto fronts) and stationarity of geostrophic linear modes onthe f-plane, but makes three extensions, namely: 1) thepossibility of higher-order accuracy, 2) no restriction to or-thogonal meshes, and 3) additional flexibility which canbe used to alter the balance between velocity and pressuredegrees of freedom to remove spurious mode branches. Wediscuss extensions to three dimensional modelling and il-lustrate the approach with numerical tests.

Colin CotterImperial Collegecolin.cotter@imperial.ac.uk.

An Edge-Based Model for Mesoscale AtmosphericDynamics

A three-dimensional semi-implicitedge-based unstructured-mesh model is developed that in-

tegrates nonhydrostatic anelastic equations, suitable forsimulation of small-to-mesoscale atmospheric flows. Themodel builds on nonoscillatory forward-in-time MPDATAapproach using finite-volume discretization and admittingunstructured meshes with arbitrarily shaped cells. Tech-nical considerations are supported with canonical simula-tions of convective planetary boundary layer, and stablystratified orographic flows. The unstructured-mesh solu-tions are compared to equivalent results generated with anestablished structured-grid model, theory and observation.

Joanna SzmelterLoughborough Universityj.szmelter@lboro.ac.uk

Piotr SmolarkiewiczNCARMMMsmolar@ucar.edu

SLIM, A Baroclinic Discontinuous Galerkin FiniteElement Model for Marine Flows: Validation onAcademic and Real Applications

Unstructured grids models for marine flow modelling areused for many years now. These models have proved theirefficiency for coastal applications. A 3D baroclinic discon-tinuous Galerkin finite element model with split-explicittime stepping, SLIM 3D, have recently been developedand applied to ideal coastal flows. This model still suf-fers problems of stability. The simulation blows up easilyon the boundaries and non-physical behaviour can be ob-served where there is a high horizontal pressure gradient.In order to fix it without changing the physics beyond themodel, a stabilized version has been developed and appliedto large-scale ocean circulation test-case, where the prob-lems of stability are crucial. This model has been comparedto other models to assess the quality of the results. Thistalk presents the SLIM model explaining its spatial andtemporal discretization characteristics. Then a large-scaleapplication in which we assess the robustness of our modelis presented. This application, a baroclinic instability ina zonally re-entrant channel, gives a comparison betweenthe SLIM model and other references. Eventually, someresults of different coastal academic and real applicationson which the model has been assessed are given.

Philippe DelandmeterEcole Polytechnique de LouvainUniversite catholique de Louvainphilippe.delandmeter@uclouvain.be

Jonathan Lambrecht, Jean-Francois RemacleUniv. catholique de LouvainBelgiumjonathan.lambrechts@uclouvain.be, jean-franois remacle¡jean-francois.remacle@uclou

158 GS13 Abstracts

J. Casey DietrichUniversity of Texas at Austindietrich@ices.utexas.edu

Modeling Three-Dimensional Processes in CoastalEngineering Applications

Irreducibly three-dimensional (and time-dependent) pro-cesses arise often enough in real-world coastal engineer-ing applications that effective tools for their solution areneeded. These processes include interaction of waves andcurrents with coastal and hydraulic structures and subsur-face air/water dynamics in heterogeneous materials. In thistalk I will discuss examples of fully three-dimensional engi-neering problems and methods for solving them directly inthree dimensions, particularly finite element and level setmethods on unstructured meshes.

Chris KeesU.S. Army Engineer Research and Development CenterCoastal and Hydraulics Laboratorychristopher.e.kees@usace.army.mil

Matthew FarthingUS Army Engineer Research and Development Centermatthew.w.farthing@usace.army.mil

Matt MalejCoastal & Hydraulics LaboratoryU.S. Army Engineer Research & Development Centermatt.malej@usace.army.mil

Roham BakhtyarUniversity of North Carolina at Chapel HillU.S. Army Engineer Research and Development Centerroham.bakhtyar@gmail.com

Steve MattisUniversity of Texas at Austinsteven@ices.utexas.edu

Efficient and Elegant Numerical Tools for OceanFlows

Numerical modelling of coastal flows is a challenging topicdue to complex topography, complex flow dynamics andlarge density variations. Such phenomena are best sim-ulated with unstructured grid models due to their highlyexible spatial discretisation. A three-dimensional discon-tinuous Galerkin finite element marine model is presented.The spatial discretisation and explicit mode splitting timeintegration scheme are described. Free surface movementis accounted for by means of an arbitrary Lagrangian Eu-lerian (ALE) moving mesh method. Mass and volume areconserved. The conservation properties and baroclinic ad-justment under gravity are tested with numerical bench-

marks. The approach exploits the topology of the 3D mesh,that is formed by stacking layers of prisms in the verticaldirection. A robust mapping between the finite differencegrid and the finite element function space is designed, tak-ing into account the discontinuities in the latter.

Mantle Convection Modelling

Mantle convection is central to understanding the largescale geologic evolution of our planet. In this contributionI will review recent progress in mantle convection modelingin my group at Munich University.

Hans-Peter BungeDepartment of Earth and Environmental Sciences, LMUMunichbunge@geophysik.uni-muenchen.de

Simulations of Thermal Convection in RotatingSpherical Shells

Di?erent implementations of several time integrators basedon our own codes and public libraries are presentedto study their e?ciency when are applied to a three-dimensional thermal convection problem in rotating spher-ical geometry. The equations are discretized with pseudo-spectral techniques. Many geophysical and astrophysicalphenomena such as the generation of the magnetic ?elds,or the di?erential rotation observed in the atmospheres ofthe major planets can be studied in this framework.

Ferran GarciaUniversitat Politecnica de Catalunya, Spainferran@fa.upc.edu

Luca BonaventuraPolitecnico di MilanoMOX, Dipartimento di Matematica F. Brioschiluca.bonaventura@polimi.it

Marta NetDepartament Fsica AplicadaUniversitat Politecnica de Catalunyamarta@fa.upc.edu

Juan SanchezUniversitat Politecnica de Catalunya, Spainsanchez@fa.upc.edu

Inverse Retrospective Problems in Geodynamics

Present geophysical and geodetic observations provide aclue to understanding the dynamics of the Earth interiorin the geological past. Data assimilation allows to con-strain the mantle flow and temperature in the past usingdynamic models and present observations. Quantitativetools are required to solve inverse retrospective problemsof geodynamics. The basic inversion methods (data as-similation methods) and their applicability to restore the

GS13 Abstracts 159

evolution of the Earth interior will be discussed.

Alik Ismail-ZadehRussian Academy of SciencesMoscow, RUSSIAaiz@ipgp.fr

Multipole Boundary Element Method in Geody-namics

We illustrate advantages and difficulties associated to theuse of Multipole-Boundary Element Method (MP-BEM) ingeodynamics. MP-BEM complements Finite Element, Vol-ume and Differences in an original way, offering solutionsto geophysical fluid-dynamic problems such as multiphase,porous media and bubbly flow, exploiting its lagrangianformulation. Applications to regional and global geody-namics are finally also shown. Mathematical and compu-tational issues are clarified in detail showing how MP-BEMis particularly suitable for parallelization on massive par-allel computers.

Gabriele MorraSchool of Earth and Environmental SciencesSeoul National Universitygabrielemorra@gmail.com

A Reduced Fracture Model for Two-Phase Flowwith Different Rock Types

In this work we are concerned with a reduced, discrete-fracture model for two-phase flow in porous medium. Wetake capillary pressure into account, and use the globalpressure formulation. We consider the case that the frac-ture and the surrounding matrix are of different rock type,that is they have different capillary pressure and relativepermeability curves. Numerical results will be presented.

Elyes AhmedInria Paris-Rocquencourtahmed elyes@yahoo.com

Amel Ben AbdaLamsin-EnitTunisieamel.benabda@enit.rnu.tn

Jean E. RobertsInria Paris-Rocquencourtjean.roberts@inria.fr

Optimizing a Cartesian Shallow Water Code onHybrid Architectures

SWE is an education-oriented code to solve the shallowwater equations on Cartesian meshes, having tsunami sim-ulation in mind as application. It is designed to supporthybrid parallelisation with multiple GPUs or co-processorssuch as Intel Xeon Phi. We will demonstrate optimisationtechniques (vectorisation, e.g.) required to achieve decent

performance, and present results on recent parallel archi-tectures.

Polymer Flooding Techniques in Enhanced Oil Re-covery

Enhanced Oil(petroleum) Recovery in petroleum reservoirsis very important now due to depleting oil reserves.This pa-per elaborates at length different method of EOR.Polymerflooding methods in depleted oil reservoirs have been enun-ciated.The mathematical equations have been developedand analysed.The analytical solutions are found.It is seenthat an increase in production upto 30% is anticipated inthis method.The bypassing of water over oil is arrested anddrag reduction enhances production.

Dr Sisir Kumar BhowmickGMIT,Balarampur,BaruipurKolkata-700144sisirkr@rediffmail.com

Numerical Modeling of Stress Fields in the Earth’sMantle with Non-Newtonian Viscosity

The spatial fields of overlithostatic pressure, the verticaland horizontal stresses in the mantle are studied in 2D nu-merical model of mantle convection. The model viscosityis temperature-, pressure-, and strain-dependent. The typ-ical overlithostatic stresses in the main part of the mantleare in the range of (7 - 9) MPa, with strong concentrationin the areas of descending slabs (up to 50 MPa). We findsignificant differences between the three studied fields.

Alexandr M. Bobrov, Alexey Baranov, Natalia BobrovaSchmidt Institute of Physics of the Eartha m bobrov@yahoo.com, aabaranov@gmail.com,a m bobrov@yahoo.com

Render the Interpolation Library SCRIPP Conser-vative

Joel ChavasCEAjoel.chavas@cea.fr

Inversion for Hydraulic Conductivity Using the

160 GS13 Abstracts

Unsaturated Flow Equations

Hydraulic conductivity (K) is a property of the soil mediaand is the main regulator of groundwater flow. However,in many hydrogeologic studies K is only known as a bulkaverage. An accurate estimate of K that is spatially consis-tent with the media is highly valuable. Here we present aninverse problem that calculates K from time-varying sat-uration (or pressure head) data; the saturation data cancome from geophysical imaging and is spatially extensive.

Rowan B. CockettUniversity of British Columbiarcockett@eos.ubc.ca

Transport Upscaling Using Coupled and Corre-lated Continuous Time Random Walks

We present a continuous time random walk (CTRW)framework for the upscaling of transport in heterogeneousmedia. The CTRW approach describes particle motions interms of a random walk in space and time. The challengeconsists in the determination of the map of the quencheddisorder that represents spatial heterogeneity, into thestochastic processes describing the space and time transi-tions. Based on stochastic models for the spatial disorder,we present two upscaling approaches: (i) for transport in acorrelated random medium, which leads to a fully coupledCTRW, and (ii) transport in correlated divergence-free ran-dom velocity fields, which leads to a CTRW characterizedby correlated random time increments. The transport be-havior is discussed in terms of first-passage time distri-butions, spatial particle distributions, and mean squareddisplacement, using random walk particle tracking simula-tions. Both sub- and superdiffusive behavior is observed.Finally, we derive the related (non-local) partial differen-tial equations for the particle densities that describe thelarge scale transport dynamics.

Marco DentzIDAEA, Spanish National Research Council (CSIC)marco.dentz@idaea.csic.es

Scale Dependent Coupling of Hysteretic CapillaryPressure, Trapping and Fluid Mobilities

We study the impact of capillary-pressure hysteresis andCO2-trapping on vertically integrated constitutive param-eter functions. Trapping is the dominant contributor tohysteresis in integrated models for the initial drainage anda following imbibition. The hysteretic nature of the cap-illary fringe is of secondary importance for advective pro-cesses. The hysteretic capillary fringe plays an importantrole for redistributive processess.

Michael A. CeliaPrinceton University

Dept of Civil Engineeringcelia@princeton.edu

Jan NordbottenDep. of Mathmatics, University of Bergenjan.nordbotten@gmail.com

Compressional Seismic Velocity Fields Parameter-ized by Haar Wavelet

Two-dimensional seismic compressional velocity fields, ex-tracted from geological models, are parameterized bymeans of Haar wavelet. The coefficients of the Haar se-ries are calculated using integral formulas. The primaryobjective of this work is to be assured that such parame-terization can represent the seismic velocity field in a satis-factory way (reasonable accuracy and few coefficients) and,then, as secondary objective, to create appropriated con-ditions to estimate wavelet coefficients by some inversionprocedure using seismic data.

Wilson M. FigueiroUniversidade Federal da BahiaInstituto de Geocienciasfigueiro@cpgg.ufba.br

Helcio PerinUniversidade do Estado da Bahia, UNEBhelciomoreira@yahoo.com.br

Adriano MartinezUniversidade Federal da Bahia, UFBAadcmartinez@hotmail.com

Saulo P. OliveiraUniversidade da Bahiasaulopo@ufpr.br

Saulo P. OliveiraUniversidade Federal do Paranasaulopo@ufpr.br

Luiz GuimaraesUniversidade Federal do Rio de Janeiro, UFRJlgg@peno.coppe.ufrj.br

Paulo CunhaCENPES-PETROBRASpemcunha@globo.com

Improvement of Convergence of Multigrid Methodin Multiphase Flow Problems.

Multigrid methods often become inefficient for solutionof multiphase flow problems because the construction ofcoarse grid operators does not take into account inhomo-geneous saturation distribution. This leads to inefficientresidual smoothing and significantly reduces convergencerate. Here we examine the convergence behavior of geomet-ric multigrid method in case when the upscaling methods(incl. multiphase) are employed in construction of coarsegrid operators. The application for nonlinear multigridmethod is also discussed.

Maxim FilatovLomonosov Moscow State University

GS13 Abstracts 161

maxfilatov89@gmail.com

Dmitry MaksimovJunior ResearcherKIAM RASdymaksimov@mail.ru

Numerical and Geometric Optimization Tech-niques for Environmental Prediction Systems

George GalanisGreek Naval AcademyUniversity of Athensggalanis@mg.uoa.gr

Polynomial Interpolation and Quadrature on Sub-regions of the Sphere

Using some recent results on trigonometric interpolationand quadrature on subintervals of the period, we presenta rule for numerical integration over some regions of thesphere, that include spherical caps and zones. The rulehas positive weights and is exact for all spherical polyno-mials of degree less or equal than n. We also constructWeakly Admissible Meshes and approximate Fekete pointsfor polynomial interpolation on such regions of the sphere.All the algorithms have been implemented in Matlab.

Mariano GentileUnaffiliatedgentimar@hotmail.it

A. Sommariva, M. Vianellotbatba@siam.org, tba@siam.org

Space-Time Wavelet Techniques in the Reverse-Time Depth Migration

A method based on the well-known reverse–time depth mi-gration and new Poincare space-time wavelets is presentedfor a smooth layered medium. We represent the forwardand back-propagated fields in terms of localized solutionscentered along rays in the medium. Initial amplitudes ofthese localized solutions on the surface are calculated bymeans of the continuous space-time wavelet analysis for theseismic data. An example with seismograms calculated bythe finite differences method is presented.

Evgeny GorodnitskiyPhysics Faculty, St.Petersburg Universityeugy@yandex.ru

Maria PerelSt. Petersburg University, Russiaperel@mph.phys.spbu.ru

Yu Geng, Ru-Shan WuUniversity of California, Santa Cruzygeng1@ucsc.edu, rwu@ucsc.edu

Statistical Characteristics, Circulation Regimesand Unstable Periodic Orbits of Simple Atmo-spheric Model

The theory of chaotic dynamical systems gives a lot of toolsthat can be used in climate studies (Lyaunov exponents,attractor dimension etc). Another potentially useful onethat could be used for the local analysis of the system PDFinvolves an expansion in terms of unstable periodic orbits(UPOs). According to it, the system statistical character-istics are approximated as a weighted sum over the orbits.The weights are inversely proportional to the orbit insta-bility characteristics so that the least unstable orbits makelarger contributions to the PDF. In our study we will try toapply the idea of UPO expansion to the simple atmosphericsystem based on the barotropic vorticity equation on thesphere. We will check how well orbits approximate the sys-tem attractor, its statistical characteristics and PDF. Theconnection of the most probable states of the system withthe UPOs will also be analyzed.

Andrey GritsunInstitute of Numerical Mathematicsandrusha@inm.ras.ru

Capillary Fracturing in Granular Media

We study the displacement of immiscible fluids in de-formable, non-cohesive granular media. Experimentally,we inject air into a thin bed of water-saturated glass beadsand observe the invasion morphology. The control parame-ters are the injection rate, the bead size, and the confiningstress. We identify three invasion regimes: capillary finger-ing, viscous fingering, and capillary fracturing, where cap-illary forces overcome frictional resistance and induce theopening of conduits. We derive two dimensionless numbersthat govern the transition among the different regimes: amodified capillary number and a fracturing number. Theexperiments and analysis predict the emergence of frac-turing in fine-grained media under low confining stress, aphenomenon that likely plays a fundamental role in manynatural processes such as primary oil migration, methaneventing from lake sediments, and the formation of desicca-tion cracks.

Mathias Trojer, Michael SzulczewskiMITtrojer@mit.edu, msulcz@mit.edu

Ruben JuanesMITCivil and Environmental Engineeringjuanes@mit.edu

Comparison Study of Spurious Wave ReflectionResponse with Staggered Finite-Volume and Un-staggered Element-Based Galerkin Schemes underMesh-Refinement

Spurious wave reflections caused by different grid sizes areexamined using both 1D linear shallow water equationsmodels based on staggered finite-volume and unstaggeredcontinuous/ discontinuous Galerkin (CG/DG) discretiza-tion. We test spurious wave reflection response causedby mesh refinement with both low and high wavenumberwave packets. Results indicate that unstaggered CG/DG

162 GS13 Abstracts

scheme produce less spurious wave reflection compared tostaggered finite-volume scheme. In particular, DG withLax-Friedrich numerical flux is completely free from spuri-ous wave reflections.

Shin-Hoo Kang, Tae-Jin OhKorea Institute of Atmospheric Prediction Systemssh.kang@kiaps.org, tj.oh@kiaps.org

A Statistical Subgrid Model for Large Eddy Simu-lations

Cinlar velocity field has been shown to represent the sub-mesoscale eddies up to 5 km in radius by an analysis ofhigh-frequency radar observations. As a result, it is pro-posed as a subgrid model for Large Eddy Simulation (LES).We consider a velocity field composed of eddies in two di-mensions using Gamma distribution for their radius. InLES, the subgrid stress is modeled based on the covariancestructure of the random velocity field.

Rukiye KaraDepartment of MathematicsMimar Sinan Fine Arts Universityrkara@msgsu.edu.tr

Mine CaglarDepartment of MathematicsKoc Universitymcaglar@ku.edu.tr

Application of a Fast Algorithm to Solving thePressure Equation Efficiently

In this talk, we will present several fast methods for solvinga non-separable elliptic pressure equation arising in porousmedia flow modeling using Darcy’s law. All of these meth-ods use a fast algorithm for solving the elliptic equation byGreen’s function method. We will present numerical resultsand compare the performance of this methods. This workis currently under progress. The research to be presentedhas been made possible by a grant (NPRP 08-777-1-141)from the Qatar National Research Fund (a member of TheQatar Foundation).

JoungDong KimTexas A&M Universityjdkim@math.tamu.edu

Craig GinTexas A&M Universitycgin@math.tamu.edu

Statistical Simlulation of Fault Zone Structures

The study demonstrates the potential use of statistical sim-ulation for describing some observed structural features ofcomplex faults zones. Deformation bands are sampled ac-cording to probability distribution based on their link todistance from the fault and fault displacement. Stochastic

modelling of fault core lens properties takes into accounttheir links to known physical constraints (i.e. host rockstratigraphy and strain distribution). Particular attentionis given to the statistical validation procedure of sampledrealizations.

Dmitriy KolyukhinCIPRBergen, Norwaydmitriy.kolyukhin@uni.no

Jan TverangerUni CIPRjan.tveranger@uni.no

New Efficient Numerical Method for Integral Equa-tions in EM Sounding of Inhomogeneous Media

The new iterative numerical method for 3d integral equa-tions of electrodynamics was devised. The main challengeof using this equations in forward problems of EM sound-ing is a need to solve a high-order system of linear equa-tions with a dense matrix. The main distinctive feature ofthe proposed method is a double integration of the elec-tric Green’s tensor in the process of algebraization of theoriginal equation to decrease the order of the matrix.

Mikhail KruglyakovLomonosov Moscow State Universitym.kruglyakov@gmail.com

Upscaling of Density-Driven Instabilities UsingCountercurrent Flow

In two-phase flow models opposite flow directions are al-lowed for the two phases in presence of density-driven flow.This countercurrent flow can be seen as macroscopic de-scription of unresolved microscopic velocities. We aim atextending the concept of countercurrent flow to upscale in-stability observed in density-driven single-phase flow mod-els that are originally described at the Darcy scale. The re-sults are included in the Multiscale Finite Volume methodto improve approximation of density-driven instabilities.

Rouven Kuenze, Ivan LunatiUniversity of Lausannerouven.kunze@unil.ch, ivan.lunati@unil.ch

Upscaling of Reactive Flows in Domains HavingRough Boundaries

We consider the flow and transport of chemically reactivesubstances in a channel over substrates having complex ge-ometry (rough boundaries). At the boundaries, the precur-sors undergo precipitation as well as dissolution. To over-come the computational complexity, we replace the roughboundary by a flat one and provide an upscaled boundarycondition. We do this for both situations: when the ge-ometry is assumed fixed (rigorous) and when the geometryvaries due to reactions (formal asymptotics).

Kundan KumarUniversity of Austink.kundan@gmail.com

GS13 Abstracts 163

Mark van HelvoortEindhoven University of Technologym.v.helvoort@student.tue.nl

Tycho van NoordenCOMSOL BVt.l.v.noorden@gmail.com

Modeling a Stochastic Convective PreciptationProcess

A simple stochastic model is used to simulate a strong con-vective precipitation process. The model includes threestochastic components: a stochastic trigger for precipi-tation state on and off (a two-state Markov jump pro-cess based on a Poisson distribution), a stochastic massflux at cloud base for a turbulence closer equation, andanother stochastic closure for neighborhood domain’s in-fluence, such as moisture convergence/divergence. Thesethree stochastic processes are tested for a single columnmodel of climate.

Kimberly LeungSan Diego State Universitykimberlydleung@gmail.com

Aneesh SubramanianUniversity of California, San Diego, USAacsubram@ucsd.edu

Samuel S. ShenSan Diego State Universityshen@math.sdsu.edu

Guang ZhangScripps Institution of Oceanographygzhang@ucsd.edu

Up-scaling Reaction Rates from Pore to Core Scale

We focus on the network flow simulation of up-scaling,from pore to core scale, of rates of anorthite and kaoli-nite reaction under acidic conditions commensurate withCO2 sequestration. The simulations allow investigation ofuncertainties in our knowledge of micro-scale reaction ratesunder flow regime as well as the flow dependence of bulkreaction rates. The results reveal the susceptibility to pre-diction errors in the case of reactions close to equilibrium.

W. Brent LindquistApplied Mathematics and Statistics, Stony BrookUniversityb.lindquist@stonybrook.edu

Daesang KimApplied Mathematics and StatisticsStony Brook Universitydaesang.kim@stonybrook.edu

Catherine Peters

Department of Civil and Environmental EngineeringPrinceton Universitycap@princeton.edu

Systems of Conservation Laws for Thermodynam-ically Consistent Adsorption with Subscale Diffu-sion and Memory Terms

Multicomponent adsorption is typically described by asystem of conservation laws in which the nonlinear fluxterms come from explicit functional relationships calledisotherms. The most popular extended Langmuir isothermis thermodynamically inconsistent. We discuss analy-sis and numerical approximation of multicomponent ad-sorption system where the thermodynamically consistentisotherms are given only implicitly, or from a coupled mi-croscopic model. We include memory terms in our modeland new examples.

F. Patricia Medina, Malgorzata PeszynskaDepartment of MathematicsOregon State Universitymedinaf@math.oregonstate.edu,mpesz@math.oregonstate.edu

A Benchmark for Thermo-Hydrological Codes onCold Regions Hydrology

Recent numerical studies proved the importance of cou-pled thermo-hydrological processes to study the evolutionof water bodies in permafrost environments under climatechange. Such coupled systems of non-linear equations (in-cluding phase change) are hard to solve and lack validationexercises. We present a benchmark of codes (numerical andexperimental test cases). It is further intended as a forumto improve the simulation performances in view of inten-sive 3D simulations including the complexity of naturalsystems.

Christophe F. GrenierLSCE - UMR8212christophe.grenier@lsce.ipsl.fr

Nicolas RouxLSCEnicolas.roux@lsce.ipsl.fr

Francois CostardIDESfrancois.costard@u-psud.fr

Emmanuel MoucheLSCEemmanuel.mouche@lsce.ipsl.fr

Geometric Characterization of Strata By InverseScattering and Active Contours

For simplicity, traditional subsurface characterizationmethods assume flat geological layers. Our approach seeksthe actual, arbitrary layer shapes that best match givensurface measurements of seismic waves. Through the mini-mization of an energy functional, active contours modelinglayer geometry evolve to the desired shape. The gradientdescent direction is derived semi-analytically for increased

164 GS13 Abstracts

computational speed. Together with the method of fun-damental solutions for numerical elastodynamic wave solu-tions, we obtain a meshfree inversion algorithm.

Martin Mueller, Francesco FedeleGeorgia Institute of Technologymartin.mueller@gatech.edu, fedele@gatech.edu

Anthony YezziGeorgia Institute of TechnologyElectrical & Computer Engr Deptayezzi@ece.gatech.edu

Identification of Seismic Quiescence Anomalies inthe Seismic Region of the Mexican Pacific Coast

We used the region-time-length (RTL) and the Schreideralgorithms to characterize seismic quiescence anomalies inthe Mexican Pacific coast. We investigated the spatiotem-poral variations of seismic quiescence prior to the past Mex-ican earthquakes of magnitude greater than 7.5 since 1970.We used an improved RTL algorithm with optimal pa-rameters. To better understand these seismic quiescenceanomalies we also studied synthetic catalogues obtainedwith a two dimensional spring-block model that mimicsthe seismic faults dynamics.

Alejandro Munoz-DiosdadoUPIBI-IPNamunozdiosdado@gmail.com

Adolfo Rudolf-NavarroESFM-IPNahrudolf@gmail.com

A Three-Scale Model of Charged Solute Transportin Swelling Clays Including Ion Size Correlations

A three-scale model is developed to describe the mix-ing of two ionic contaminants in swelling clays. Thenanoscopic problem arises from the Statistical Mechan-ics and is governed by an integral Fredholm equation forthe ion/nanopore correlation function coupled with Poissonproblem for the electric potential. Swelling of the clustersis coupled microscopically with the diffusion of the speciesin the micro-pores and the homogenization procedure is ap-plied to up-scale the microscopic model to the macroscale.

Dung Le, Christian MoyneUniversite de Lorraine, LEMTA, UMR 7563,Vandoeuvre les Nancy, Francedung.le@univ-lorraine.fr, christian.moyne@univ-lorraine.fr

Marcio A. MuradNational Laboratory of Scientific ComputationLNCC/MCTmurad@lncc.br

Sidarta LimaFederal University Rural of Rio deJaneirosidarta@lncc.br

Continuum Darcy Approach for Coupling Surface-

Subsurface Flows: Application to Heterogeneousand 3D Configurations

A fully integrated coupling between surface and subsurfaceflows has been implemented recently (Weill et al., 2009).This model unifies the Richards and the diffusive waveequations into a single generalized Richards equation de-fined in a single domain composed of surface and subsurfacesubdomains. This model has been applied successfully to2D configurations. We will show some improvements of thescheme to simulate the runon-runoff process on a hetero-geneous soil and 3D configurations.

Claude Mugler

CEA / LSCEclaude.mugler@cea.fr

Emmanuel MoucheCEA, DRNFranceemmanuel.mouche@cea.fr

Cecile CarrereCNRS / LSCEcecile.carrere@lsce.ipsl.fr

Large Scale Patterns in Convection: fromRayleigh-Benard, Through Prandtl Problem, toMoist Atmospheric Convection

Large scale patterns formation in dry and moist convectionscenarios are addressed in this paper. The first part of thetalk will be devoted to the case of clustering of plumesin Rayleigh-Benard convection: through a two-scale pro-cess, kinetic energy is transferred mainly to low horizontalwave numbers while the sizes of individual plumes remainon the scale of the boundary layer thickness. Again in adirect numerical simulation framework, the study of thePrandtl problem is addressed as a simpli?ed model of dryatmospheric convection, kept in statistically stationary ra-diativeconvective equilibrium. Finally the emergence andtemporal evolution of large-scale spatial-temporal oscillat-ing modes in deep moist convection, for an atmospherein radiative-convective equilibrium. To this end, we usecloud-resolving numerical simulations of the convective at-mosphere at very high resolution and on a very large do-main, using WRF model in LES mode.

Antonio ParodiIstituto di Scienze dell’Atmosfera e del Climaantonio.parodi@cimafoundation.org

Multiphysics, Multiscale Network Modeling of GasTransport in Mudrocks

Despite recent research activity, shale petrophysics remainselusive due to the difficulties in experimental and numeri-cal analysis of length scales below 100nm. We implementa network model with both micron and nanometer scalepores that includes effects of convection, diffusion as wellas sorption of gas on pore walls. Diffusion and sorptionhave a significant impact on ultimate gas permeability, andthe magnitude of the effect depends on pore connectivity,network geometry and size distribution.

Masa ProdanovicUniversity of Texas at Austin

GS13 Abstracts 165

Department of Petroleum and Geosystems Engineeringmasha@ices.utexas.edu

Ayaz MehmaniUniversity of Texas at Austinmehmani.ayaz@gmail.com

Explicit Modeling of Fault Damage Zone Proper-ties

This work aims to capture realistic damage zone featuresexplicitly in reservoir models. A separate fault zone grid isgenerated from a conventional reservoir model and sub-sequently populated with damage zone properties usingan extensive dataset of deformation band densities andpermeability collected from outcrops. The resulting faultzone grid populated is subsequently merged with the orig-inal conventional model, and comparison of flow behaviorof this merged model and the conventional model is con-ducted.

Dongfang QuUni CIPRUniversity of Bergendongfang.qu@uni.no

Jan TverangerUni CIPRjan.tveranger@uni.no

Per RøeNorwegian Computing Centreper.re@nr.no

Applied Precipitation Nowcast

We present a reliable precipitation nowcasting systemwhich operates on radar data. The computational methodis an extension of the McGill Algorithm for PrecipitationNowcasting by Lagrangian Extrapolation (MAPLE), whichprovides a fast and accurate forecast by semi-Lagrangianadvection and near-optimal wavelet filtering. Our imple-mentation provides near real-time computation and we ex-tend MAPLE by using level sets for the computation ofprecipitation areas and optical flow methods for the com-putation of advection vector fields.

Thorsten RiessW3 Data GmbHriess@w3-data.de

Meshless Techniques for Anisotropic DiffusionProblems

Solving anisotropic diffusion equations is an important taskfor many problems in Geosciences. We compare the effi-ciency of two meshless techniques based upon the MeslessLocal Petrov–Galerkin (MLPG) framework. The fist tech-nique is an MLPG method with suitable test and trial func-tions; the latter is based on the Generalized Moving LeastSquares method. By numerical experiments we show thatboth methods can solve highly anisotropic problems.

Flavio SartorettoUniversita’ Ca’ Foscari Venezia

DAISflavio.sartoretto@unive.it

Annamaria Mazzia, Giorgio PiniUniversita’ di PadovaDICEAannamaria.mazzia@unipd.it, giorgio.pini@unipd.it

Numerical Approximation of Reactive Flow inPorous Media with Discontinuous Reaction.

We present a numerical method for the simulation of reac-tive flows in porous media characterized by a discontinuityin the reaction term. The strategy is based on an oper-ator splitting that decouples the reaction from advectionand diffusion, so that it can be approximated with tailoredtime integration schemes that guarantee accuracy even inthe case of discontinuous right hand sides.

A Fully Implicit Solver for Geochemical Processesin Compacting Basins.

Geochemical processes such as quartz precipitation andillite-smectite transformation play a major role in deter-mining porosity and permeability in compacting basins.We present a fully implicit method for the simulation oftemperature, pressure and porosity evolution in the pres-ence of mechanical and geochemical compaction. The im-plicit approach is compared with an iterative decoupling ofthe equations to assess the better performances of the firststrategy in cases characterized by strong overpressures.

Ilaria ImperialiMox, Department of Mathematics, Politecnico di Milanoimperiali.ilaria@gmail.com

Semi Lagrangian Methods in Variable Density Flow

We present a 3D model for transient groundwater flow in aconfined aquifer based on discretized flow and solute massbalance equations. To overcome the difficulty of couplednonlinear governing equations a Semi - Lagrangian methodis implemented for the solute transport equation. This en-ables to choose arbitrarily large time step without losingstability, reduce numerical diffusion and also keep the sys-tem mass conservative.

Klara SteklovaUniversity of British ColumbiaDepartment of Earth, Ocean and Atmospheric Sciencesklara.steklova@gmail.com

166 GS13 Abstracts

Investigation of Instability of Displacement Frontin Flow Problems

The problem of two-phase immiscible fluid flow is consid-ered, including sources and dependence of viscosity on tem-perature. Numerical calculations were achieved for differ-ent values of temperature and with increasing temperature,oil viscosity decreases exponentially and the stable state ispossible. Additionally to the front stability there is an in-crease in the rate of displacement oil and increasing of pro-duction rate. Selecting optimal temperatures of injectedfluid is a way for intensification of the field development.

Natalia SyulyukinaLomonosov Moscow Sate Universitynsyulyukina@gmail.com

Pore-Scale Modeling and Experimental Investiga-tions of Mixing-Controlled Geochemical and Bio-logical Reactions

Many important applications in geosciences and ground-water pollution require understanding of mixing-controlledgeochemical and microbiological reactions that affectporosity through mineral precipitation/dissolution andbiofilm growth. We study these coupled processes usingpore-scale simulation and micro-fluidics laboratory experi-ments. We use the lattice Boltzmann method to solve forsingle-phase fluid flow, the finite volume method to solvefor multi-species reactive transport, and a cellular automa-ton method for porosity evolution. Direct numerical simu-lations are compared with laboratory experiments.

Albert J. Valocchi, Youneng Tang, Haihu LiuUniversity of Illinois at Urbana-Champaignvalocchi@illinois.edu, tayone09@illinois.edu,haihuliu@illinois.edu

Hongkyu YoonGeoscience Research and ApplicationsSandia National Laboratorieshyoon@sandia.gov

A Multiscale Time Integrator for Computing Long-wave Shallow Water Flows at Low Froude Numbers

A new multilevel semi-implicit scheme for the computa-tion of low Froude number shallow water flows is presented.Motivated by the needs of atmospheric flow applications,it aims to minimize dispersion and amplitude errors in thecomputation of long wave gravity waves. While it correctlybalances ”slaved” dynamics of short-wave solution com-ponents induced by slow forcing, the method eliminatesfreely propagating compressible short-wave modes, whichare under- resolved in time.

Stefan VaterUniversity of Hamburg, KlimaCampusstefan.vater@zmaw.de

Rupert KleinFreie Universitat Berlinrupert.klein@math.fu-berlin.de

Efficient Solver for Transversely Isotropic EikonalEquation Using Perturbation Theory

Numerical solutions of the eikonal (Hamilton-Jacobi) equa-tion for transversely isotropic (TI) media are essential forimaging and tomography applications. Such solutions,however, suffer from the inherent higher-order nonlinearityof the TI eikonal equation, which requires solving a quar-tic polynomial at each computational step. Using pertur-bation theory, we approximate the first-order discretizedform of the TI eikonal with a series of simpler equationsfor the coefficients of a polynomial expansion of the eikonalsolution in terms of the anellipticity anisotropy parameterη. In addition to achieving very high accuracy, the formu-lation allows tremendous cost reduction compared to theexact TI eikonal solver. We demonstrate these assertionsthrough tests on a homogeneous TI model, the VTI Mar-mousi model, and the BP TTI model.

Umair bin Waheed, Tariq AlkhalifahKing Abdullah University of Science and Technologyumairbin.waheed@kaust.edu.sa,tariq.alkhalifah@kaust.edu.sa

Adaptive Multi-Scale/physics Modeling of Two-Phase Flow Including Capillary Pressure

Important applications in porous media require large-scalesimulation. To capture important effects high spatial res-olution can be necessary leading to enormous computa-tional costs. One solution strategy are multi-scale meth-ods, which decrease the global degrees of freedom whilepreserving important features. We present an approach,which is applicable in a wide range of flow regimes, also ifcapillary pressure effects are significant. It combines adap-tive grid methods based on MPFA with local upscalingtechniques.

Markus WolffUniversity of StuttgartGermanymarkus.wolff@iws.uni-stuttgart.de

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