1. An Advanced Simulation and Computing (ASC) Academic Strategic Alliances Program (ASAP) Center at The University of Chicago The Center for Astrophysical Thermonuclear Flashes Hydro and other key algorithms and A few issues/tricks of the trade Alan Calder May 13, 2004

2. The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago What I do and will try to answer questions about  Basic physics:  fluid instabilities (Rayleigh-Taylor)  radiation transport  Astrophysics  Novae: 2-d models of breaking gravity waves (a model for envelope enrichment)  Type Ia supernovae: hydrostatic equilibrium, hydrodynamics, self- gravity, reactive flow.

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

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

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

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

7. 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

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

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

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

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

12. 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

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

14. 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…

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

16. 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

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

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

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

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

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

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

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

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

25. The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Single-mode 3-d Rayleigh-Taylor Density (g/cc) 48163264128 (grid points) t = 3.1 sec 256

26. The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Fluid Instabilities in Astrophysics  Observations of astrophysical phenomena, e.g. 56 Co in SN 1987A, indicate that fluid instabilities can play an important role STScI

27. 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.

28. The ASC/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago 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 Dwarkadas et al. astro-ph/0403109