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Hydro and other key algorithms and A few issues/tricks of the trade

This publication delves into crucial topics like fluid instabilities in astrophysics, Type Ia supernovae modeling, and hydrodynamics methods like PPM. It includes insights on radiation transport, Euler Equations, and finite volume hydrodynamics modules. The text explores various algorithms and validation tests in theoretical astrophysics simulations. The author sheds light on challenges such as numerical diffusion and the importance of refining criteria in simulations for accurate results.

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Hydro and other key algorithms and A few issues/tricks of the trade

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  1. Hydro and other key algorithmsandA few issues/tricks of the trade Alan Calder May 13, 2004

  2. 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. Euler Equations

  4. Internal Energy Advection

  5. Multiple Species

  6. Hydrodynamics Modules

  7. Finite Volume Hydrodynamics Method (PPM) Divide the domain into zones that interact with fluxes

  8. Fluxes at jumps in mesh refinement

  9. Riemann Problem: Shock Tube Initial conditions: a discontinuity in density and pressure

  10. Riemann Problem: Shock Tube World diagram for Riemann problem

  11. Riemann Problem: Shock Tube PPM has special algorithms for these features

  12. Verification Test: Sod Shock Tube Demonstrates expected 1st order convergence of error

  13. Verification Test: Isentropic Vortex Demonstrates expected 2nd order convergence of error

  14. Sod Tube W/ AMR Demonstrates expected 1st order convergence of error, but…

  15. Riemann Problem: Convex EOS

  16. New Validation Results: Vortex-dominated Flows • “Cylinder” of SF6 hit by Mach 1.2 shock LANL

  17. Shocked Cylinder Experiment • Snapshots at 50, 190, 330, 470, 610, 750 ms

  18. New Validation Results: Vortex-dominated Flows Visualization magic from ANL Futures Lab

  19. Shocked Cylinder Simulations

  20. 4 shock problem

  21. 4 contact problem

  22. Three-layer Target Simulation Movie

  23. Three-layer Target Simulation Comparison to Experiment

  24. Three-layer Target Simulation Convergence results: percent difference

  25. l (grid points) Single-mode 3-d Rayleigh-Taylor Density (g/cc) 4 8 16 32 64 128 256 t = 3.1 sec

  26. Fluid Instabilities in Astrophysics • Observations of astrophysical phenomena, e.g.56Co in SN 1987A, indicate that fluid instabilities can play an important role STScI

  27. 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. 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

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