280 likes | 284 Vues
Hydro and other key algorithms and A few issues/tricks of the trade. Alan Calder. May 13, 2004. What I do and will try to answer questions about. Basic physics: fluid instabilities (Rayleigh-Taylor) radiation transport Astrophysics
E N D
Hydro and other key algorithmsandA few issues/tricks of the trade Alan Calder May 13, 2004
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.
Finite Volume Hydrodynamics Method (PPM) Divide the domain into zones that interact with fluxes
Riemann Problem: Shock Tube Initial conditions: a discontinuity in density and pressure
Riemann Problem: Shock Tube World diagram for Riemann problem
Riemann Problem: Shock Tube 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…
New Validation Results: Vortex-dominated Flows • “Cylinder” of SF6 hit by Mach 1.2 shock LANL
Shocked Cylinder Experiment • Snapshots at 50, 190, 330, 470, 610, 750 ms
New Validation Results: Vortex-dominated Flows Visualization magic from ANL Futures Lab
Three-layer Target Simulation Comparison to Experiment
Three-layer Target Simulation Convergence results: percent difference
l (grid points) Single-mode 3-d Rayleigh-Taylor Density (g/cc) 4 8 16 32 64 128 256 t = 3.1 sec
Fluid Instabilities in Astrophysics • Observations of astrophysical phenomena, e.g.56Co in SN 1987A, indicate that fluid instabilities can play an important role STScI
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 Dwarkadas et al. astro-ph/0403109