the physics of flash and a few issues/tricks of the trade

An Advanced Simulation and Computing (ASC) Academic Strategic Alliances Program (ASAP) Center

at The University of Chicago

The Center for Astrophysical Thermonuclear Flashes

The physics of Flashand

A few issues/tricks of the trade

Alan Calder

June 4, 2006

The ASC/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

The FLASH Code

Cellular detonation

Compressed turbulence

Helium burning on neutron stars

Richtmyer-Meshkov instability

Laser-driven shock instabilitiesNova outbursts on white dwarfs Rayleigh-Taylor instability

Flame-vortex interactions

Gravitational collapse/Jeans instability

Wave breaking on white dwarfs

Shortly: Relativistic accretion onto NS

Orzag/Tang MHDvortex

Type Ia Supernova

Intracluster interactions

MagneticRayleigh-Taylor

The FLASH code1. Parallel, adaptive-mesh simulation code2. Designed for compressible reactive flows3. Ideal, Resistive, and Hall MHD (Cartesian coords)4. Has a modern CS-influenced architecture5. Can solve a broad range of (astro)physics problems6. Portable- runs on many massively-parallel systems6. Scales and performs well- Gordon Bell prize7. Is available on the web: http://flash.uchicago.edu8. Flash 3 now (pre-)alpha released!


Hydrodynamics

PPM hydrodynamics based on the Prometheus code of Fryxell.

Directionally split, direct Eulerian implementation of Colella and Woodward (1984) that allows for non-ideal gasses (Colella and Glaz 1985).

2nd-order Strang split in time.

Solves Euler equations for inviscid compressible hydrodynamics in 1, 2, and 3 dimensions and several geometries (Cartesian, 2-d cylindrical, 1-d spherical)

Other `flavors’ of PPM may be released.


Hydrodynamics

Contact steepener controlled by parameter use_steepening.

Modified states version for use in simulations of objects in hydrostatic equilibrium. Contribution to pressure in Riemann solver from gravity removed. Parameter ppm_modifiedstates.

Interpolation/monotonization procedure of PPM can introduce errors in abundances of species. There is an implementation of the consistent mass advection method of Plewa and Muller (1999). Parameter use_cma_flattening.

Odd/even instability can occur when shocks are aligned with the grid (Quirk 1997). Fix is to switch to HLLE solver in shocks. Parameter hybrid_riemann. Test problem odd_even.


Euler Equations w/gravity


Internal Energy Advection


Multiple Species


Relativistic Hydrodynamics

Module based on the Pluto code of A. Mignone.

Extension to PPM.

1-, 2-, and 3-d Cartesian, 2-d cylindrical, 1-d spherical geometries

Ideal gas EOS

Directionally split version of Mignone et al. 2005 implemented in Flash.


MHD

Based on a finite-volume cell-centered method proposed Powell et al. 1999.

Ideal, Resistive, Hall MHD in Cartesian coords.

Works with other modules: self-gravity, multi-species, burning, general EOS.

Verified against standard benchmarks: MHD shock tube, Brio-Wu problem, shock-cloud, Orszag-Tang problem.

Details of resistive MHD in Malyshkin, Linde et al. (2005)

Dongwook Lee coming to Flash soon!


Equations of state


Equations of state

“Helmholtz” EOS for degenerate plasma (stellar material)

P = Pion + Prad + Pele + Ppos + Pcoul

Pion = ideal = 5/3 gas for ionized nuclei

Prad = blackbody = 1/3 aT4

Pele and Ppos = non-interacting Fermions

Pcoul = correction for Coulomb interactions between ions and the surrounding e- gas

Fryxell et al. (2000), Timmes and Arnett (1999)


Source Terms

Nuclear reactions

7 nuclide “-chain” + Si burning network

13 nuclide “-chain” + heavy-ion network

19 nuclide “-chain” + heavy-ion + H burning network

Someday a general network?

Non-equilibrium Ionization

Stirring

Heating


Aside: Mesh Adaptivity and R-T Instability


Finite Volume Hydrodynamics Method (PPM)

Divide the domain into zones that interact with fluxes


Fluxes at jumps in mesh refinement


Riemann Problem: Shock Tube

Initial conditions: a discontinuity in density and pressure



World diagram for Riemann problem



PPM has special algorithms for these features


Verification Test: Sod Shock Tube

Demonstrates expected 1st order convergence of error


Verification Test: Isentropic Vortex

Demonstrates expected 2nd order convergence of error


Sod Tube W/ AMR

Demonstrates expected 1st order convergence of error, but…


Riemann Problem: Convex EOS


New Validation Results: Vortex-dominated Flows

“Cylinder” of SF6 hit by Mach 1.2 shockLANL


Shocked Cylinder Experiment

Snapshots at 50, 190, 330, 470, 610, 750 s


New Validation Results: Vortex-dominated Flows

Visualization magic from ANL Futures Lab


Shocked Cylinder Simulations


4 shock problem


4 contact problem


Single-mode 3-d Rayleigh-Taylor

Density (g/cc)4 8 16 32 64 128 (grid points) t = 3.1 sec

256


Boundary Condition

Construct divide_domain for a particular problem


Summary/Conclusions

Numerical diffusion is a resolution-dependent effect that can significantly alter results.

Care must be taken when adding physics to hydro (e.g. convex EOS)

AMR is tricky.

Need right balance between computational savings and accuracy of solution.

Refinement criteria are problem-dependent and can affect the results of simulations.


Bibliography

T. F. M.

Fryxell et al., ApJS, 131 273 (2000)

Calder et al., in Proc. Supercomputing 2000, sc2000.org/proceedings

Calder et al., ApJS, 143 201 (2002)

Plewa and Muller, A&A, 142, 349 (1999)

Mignone, Plewa, and Bodo, ApJS, 160 199 (2005)

Powell et al. JCP, 154, 284 (1999)

Timmes & Arnett ApJS, 125, 294 (1999)

Malyshkin, Linde, & Kulsrud, Phys. Plasmas, 12 (10), 102902, 2005 astro-ph/0508094

the physics of flash and a few issues/tricks of the trade

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