Hydro and other key algorithms and A few issuestricks of the trade

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Hydro and other key algorithmsandA few
issues/tricks of the trade

• Alan Calder

May 13, 2004
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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.

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Euler Equations
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Internal Energy Advection
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Multiple Species
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Hydrodynamics Modules
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Finite Volume Hydrodynamics Method (PPM)

• Divide the domain into zones that interact with
  fluxes

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Fluxes at jumps in mesh refinement
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Riemann Problem Shock Tube

• Initial conditions a discontinuity in density
  and pressure

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Riemann Problem Shock Tube

• World diagram for Riemann problem

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Riemann Problem Shock Tube

• PPM has special algorithms for these features

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Verification Test Sod Shock Tube

• Demonstrates expected 1st order convergence of
  error

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Verification Test Isentropic Vortex

• Demonstrates expected 2nd order convergence of
  error

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Sod Tube W/ AMR

• Demonstrates expected 1st order convergence of
  error, but

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Riemann Problem Convex EOS
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New Validation Results Vortex-dominated Flows

• Cylinder of SF6 hit by Mach 1.2 shock

LANL
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Shocked Cylinder Experiment

• Snapshots at 50, 190, 330, 470, 610, 750 ms

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New Validation Results Vortex-dominated Flows

• Visualization magic from ANL Futures Lab

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Shocked Cylinder Simulations
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4 shock problem
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4 contact problem
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Three-layer Target Simulation

• Movie

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Three-layer Target Simulation

• Comparison to Experiment

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Three-layer Target Simulation

• Convergence results percent difference

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Single-mode 3-d Rayleigh-Taylor

• Density (g/cc)

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8
16
32
64
128
256
t 3.1 sec
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Fluid Instabilities in Astrophysics
STScI

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

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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.

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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