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 Flash and A few issues/tricks of the trade Alan Calder June 4, 2006

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago The FLASH Code Cellular detonation Compressed turbulence Helium burning on neutron stars Richtmyer-Meshkov instability Laser-driven shock instabilities Nova 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 MHD vortex Type Ia Supernova Intracluster interactions Magnetic Rayleigh-Taylor The FLASH code 1.Parallel, adaptive-mesh simulation code 2.Designed for compressible reactive flows 3.Ideal, Resistive, and Hall MHD (Cartesian coords) 4.Has a modern CS-influenced architecture 5.Can solve a broad range of (astro)physics problems 6.Portable- runs on many massively-parallel systems 6.Scales and performs well- Gordon Bell prize 7.Is available on the web: 8.Flash 3 now (pre-)alpha released!

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago 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). 2 nd -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.

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago 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.

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Euler Equations w/gravity

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Internal Energy Advection

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Multiple Species

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago 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 implemented in Flash.

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago MHD Based on a finite-volume cell-centered method proposed Powell et al 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!

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Equations of state

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Equations of state “Helmholtz” EOS for degenerate plasma (stellar material) P = P ion + P rad + P ele + P pos + P coul P ion = ideal  = 5/3 gas for ionized nuclei P rad = blackbody = 1/3 aT 4 P ele and P pos = non-interacting Fermions P coul = correction for Coulomb interactions between ions and the surrounding e - gas Fryxell et al. (2000), Timmes and Arnett (1999)

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

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Aside: Mesh Adaptivity and R-T Instability

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Finite Volume Hydrodynamics Method (PPM) Divide the domain into zones that interact with fluxes

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Fluxes at jumps in mesh refinement

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Riemann Problem: Shock Tube Initial conditions: a discontinuity in density and pressure

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Riemann Problem: Shock Tube World diagram for Riemann problem

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Riemann Problem: Shock Tube PPM has special algorithms for these features

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Verification Test: Sod Shock Tube Demonstrates expected 1 st order convergence of error

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Verification Test: Isentropic Vortex Demonstrates expected 2 nd order convergence of error

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Sod Tube W/ AMR Demonstrates expected 1 st order convergence of error, but…

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Riemann Problem: Convex EOS

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago New Validation Results: Vortex-dominated Flows “Cylinder” of SF 6 hit by Mach 1.2 shock LANL

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Shocked Cylinder Experiment  Snapshots at 50, 190, 330, 470, 610, 750  s

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago New Validation Results: Vortex-dominated Flows Visualization magic from ANL Futures Lab

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Shocked Cylinder Simulations

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago 4 shock problem

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago 4 contact problem

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Three-layer Target Simulation

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Three-layer Target Simulation Comparison to Experiment

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Three-layer Target Simulation Convergence results: percent difference

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Single-mode 3-d Rayleigh-Taylor Density (g/cc) (grid points) t = 3.1 sec 256

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Boundary Condition Construct divide_domain for a particular problem

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago 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.

The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Bibliography T. F. M. Fryxell et al., ApJS, (2000) Calder et al., in Proc. Supercomputing 2000, sc2000.org/proceedings Calder et al., ApJS, (2002) Plewa and Muller, A&A, 142, 349 (1999) Mignone, Plewa, and Bodo, ApJS, (2005) Powell et al. JCP, 154, 284 (1999) Timmes & Arnett ApJS, 125, 294 (1999) Malyshkin, Linde, & Kulsrud, Phys. Plasmas, 12 (10), , 2005 astro-ph/