opportunities montes i
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Magma Dynamics at CIGLaurent G. J. Montsi
University of MarylandContributions from:
Marc Spiegelman (Columbia)
Steve Quenette, David Lee (VPAC)
Wolfgang Bangerth (Texas A&M)
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Why Magma Dynamics? Probe into the mantle
Flux influenced bygeodynamics (temperature,flow, pressure)
Composition depends onsource and transport process
Complements geological andgeophysical investigation
Influences mantledynamics
Diferentiation / partitioningof heat producing elements
Buoyancy of melt andresiduum
Melt distributionmodel underneathultraslow ridgesMontsi, Hebert,
Behn, Barry, 2009
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A multiphysics problem Two-phase flow McKenzie 1984 formulation
Flow of melt controlled byDarcys law
Compaction of matrixcontrolled by bulk viscosity Stokes flow
Additional complexity Surface tension, grain boundary
processes, viscoelasticity,failure, thermodynamics
Use magma dynamics astestbed for multiphysicssoftware
10 m
Granitic melt in quartz(Laporte et al. 1997)
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Magma equations
t+V = 1 ( )
P
+
s
KP+ P
= K
P* + g[ ] +
fs
P*= V+ V
T( ) g
V =P
P = s0gz +P+ P
*
v = VK
P
*+P( )+ g[ ]
K=K0
n
Solve for , V, P, P*
Compute other variables
Spiegelman, Katz, and Simpson, 2007
Mass Conservation
Compressibility
Darcy/Helmholtz
Stokes
Permeability
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The MaDDs project Magma Dynamics Demonstration Suite 5 demonstration problems, described in
online document at CIG
1: 2D ridge / 3D segmented ridge (Stokes only) 2: Constant porosity ridge (Stokes + Darcy) 3: Shear bands 4: Solitary wave (Darcy flow + compaction)
5: Coupled ridge, forced melting
Test several software libraries / platforms No Gold Standard code!
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MaDDS platforms / software stgMaDDS project
David Lee (VPAC) Based on StGermain
Deal.II Wolgang Bangerth (TAMU) Adaptive mesh refinement
MultiMaDDS: Laurent Montsi (Maryland) COMSOL multiphysics
FEniCS/PETSc hybrid Marc Spiegelman (Columbia) Automatic code generation
MaDDS-2: Stokes flow anduniform porosity melt migration
(COMSOLTM, Montsi.)
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Status of stgMaDDS Most problems done
Stokes benchmark Constant porosity
ridge
Solitary wave Ridge with melting
Alpha versionreleased throughCIGs mercurialrepository andStGermain project
Compaction pressure for MaDDS-5: Fullycoupled 3D segmented isoviscous ridgewith melting. (Quenette and Lee one-pager)
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Commercial multiphysicssoftware
COMSOL Multiphysics 3D Stokes Flow, Darcy
flow, and Helmholtzequation all implemented
Possibility of adaptivemeshing (steady-state),ALE, other physics
Evaluation Great for small, rapid
applications.
Easy to learn, even withlittle numerical knowledge
Cant tinker with solver
MaDDS-2 with COMSOL
Multiphysics (Montsi)
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MultiMaDDS status MaDDS-1: Stokes solver
Higher order element Unstructured mesh (ALE and AMR
possible)
Stress and temperature dependentrheology (with Mark Behn)
MaDDS-2: Stokes coupled withDarcy equation
MaDDS-4: Solitary waves: CustomPDE and Helmholtz equation
2D and 3DStokes flow and uniformporosity melt migration with
COMSOL MultiphysicsTM
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FEniCS/PETSc hybrid Developed by Marc Spiegelman Automated code generation (FFC/Dolfin) and
PDE-based block-preconditioners (PETSc)
MaDDS 1, 2, 4 done; Preliminary MaDDS-5
MaDDS-2 with FEniCS/PETSc
_ Stokes flow with cornerflow boundary conditions_ Melt trajectory for constantporosity
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MaDDS-4: Solitary wave (FEniCS)
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Adaptive refinement Deal.II (Bangerth)
Existing Darcy flow tutorials Stokes flow tutorial complete:
Step 22
Compaction equation underdevelopmentStokes flow forsegmented ridge withadaptive refinement(Burstedde et al.)
Deal.II tutorial step 22
3D Stokes flow underneath a ridge
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Summary / Evaluation
StGermain Flexible, but complex
COMSOLMultiphysics
Easy to use butimpossible to modify
Limited to smallproblems
FEniCS/PETSc Newly adopted: Stay
tuned!
Deal.II Flexible library Excellent tutorials
Multiphysics is a challenge! No ideal solution
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Possible future goals Multiphysics coupling
Mantle convection Tectonics
Rheology/failure Computational
thermodynamics
Adaptive refinement Deal.ii step 22 adaptively refinedmesh (Bangerth, 2008)
Mid-ocean ridge tectonics influences by dike intrusion
Tucholke, Behn, Buck, 2008