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Center for Radiative Shock Hydrodynamics Fall 2011 Review. Code Comparison and Validation LA-UR 11- 04905 Bruce Fryxell. Code comparison collaboration includes researchers from three institutions. CRASH – University of Michigan Bruce Fryxell, Eric Myra Flash Center – University of Chicago

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center for radiative shock hydrodynamics fall 2011 review

Center for Radiative Shock HydrodynamicsFall 2011 Review

Code Comparison and Validation

LA-UR 11-04905

Bruce Fryxell

code comparison collaboration includes researchers from three institutions
Code comparison collaboration includes researchers from three institutions
  • CRASH – University of Michigan
    • Bruce Fryxell, Eric Myra
  • Flash Center – University of Chicago
    • MiladFatenejad, Don Lamb, Carlo Grazianni
  • Los Alamos National Laboratory
    • Chris Fryer, John Wohlbier
the crash problem has inspired this collaboration
The CRASH problem has inspired this collaboration

When output from H2D at 1.1 ns is used as the initial conditions for CRASH, the primary shock is not planar, but shows a large protruding feature at the center of the tube

Wall shock appears similar to that seen in experiments

we are comparing several hedp codes
We are comparing several HEDP codes
  • Codes currently in the test suite
    • CRASH (University of Michigan)
    • FLASH (University of Chicago)
    • RAGE, CASSIO (LANL)
    • HYDRA (LLNL)
  • Our goal is to understand differences between results of the CRASH experiment and simulations
  • This will be accomplished by comparing the codes on a wide range of problems, from simple tests to full HEDP experiments
the codes in the test suite cover a range of numerical algorithms and physics models
The codes in the test suite cover a range of numerical algorithms and physics models
  • Grid
    • CRASH – Eulerian AMR, block structured
    • FLASH – Eulerian AMR, block structured
    • RAGE/CASSIO – Eulerian AMR, cell-by-cell refinement
    • HYDRA – ALE (Arbitrary Lagrangian-Eulerian)
  • Hydrodynamics
    • CRASH – Second-order Godunov, dimensionally unsplit
    • FLASH – Piecewise-Parabolic Method, Strang splitting
    • RAGE/CASSIO – Second-order Godunov
    • HYDRA – Lagrangian with remap
treatment of material interfaces differs significantly between the codes
Treatment of material interfaces differs significantly between the codes
  • CRASH
    • Level set method – no mixed cells
  • FLASH
    • Separate advection equation for each species
    • Interface steepener - consistent mass advection algorithm
    • Opacities in mixed cells weighted by number density
    • Common Tiin each cell used to compute other quantities
  • RAGE/CASSIO
    • Interface preserver or volume of fluid
    • Opacities in mixed cells weighted by number density
    • EOS in mixed cells assume temperature and pressure equilibration
  • HYDRA
    • No mixed cells in Lagrangian mode
both radiative diffusion and transport are represented in the test suite
Both radiative diffusion and transport are represented in the test suite
  • Radiative Transfer
    • CRASH / FLASH / RAGE
      • Multigroup flux-limited diffusion
      • Emission term treated explicitly (implicitly in CRASH)
      • Equations for electron energy and each radiation group advanced separately
      • CRASH includes frequency advection
      • RAGE uses implicit gray calculation for radiation/plasma energy exchange
    • CASSIO
      • Implicit Monte Carlo
    • HYDRA
      • Multigroup flux-limited diffusion
      • Emission term treated implicitly
      • Equations for electron energy and each radiation group advanced simultaneously
      • Implicit Monte Carlo (not yet exercised for this study)
a variety of three temperature methods and drive sources are included
A variety of three-temperature methods and drive sources are included
  • Three-temperature approach
    • CRASH / FLASH / RAGE / CASSIO
      • Compression/shock heating divided among ions, electron, and radiation in proportion to pressure ratios
      • FLASH has option to solve separate electron entropy equation to apply shock heating only to ions
    • HYDRA
      • Only ions are shock heated by adding an artificial viscous pressure to the ion pressure
  • Drive source
    • CRASH – Laser drive from Hyades, X-ray drive, laser package
    • FLASH – X-ray drive, laser package under development
    • RAGE – X-ray drive, laser package under development
    • CASSIO – Mono-energetic photons
    • HYDRA – Single-beam laser
first code comparison attempt was the 1d shifted problem
First code comparison attempt was the “1d shifted problem”

One-dimensional version of the CRASH problem shifted into a frame of reference in which the Be disk is stationary

results on 1d shifted problem have led us to consider a suite of simpler tests
Results on 1D shifted problem have led us to consider a suite of simpler tests
  • Temperature relaxation tests
  • Diffusion tests
    • Conduction
    • Radiative diffusion
  • Hydrodynamic tests

These tests are still in progress – some tests have been completed with only a subset of the code suite, while others have not yet been attempted with any of the codes

temperature relaxation tests
Temperature relaxation tests
  • Initial conditions
    • Infinite Medium – no spatial gradients
    • Ion, electron, and radiation temperatures initialized to different values
    • Fully ionized helium plasma with density 0.0065 gm/cm3
    • Gamma-law EOS
  • Individual tests
    • Ion/Electron equilibration
    • Ion/Electron equilibration + radiation
      • Constant opacity
      • Electron-temperature-dependent opacity
      • Energy-group-dependent opacity
        • 4 groups or 8 groups
        • Constant (but different) opacity in each group
crash flash and rage give identical results for the simplest relaxation problems
CRASH, FLASH and RAGE give identical results for the simplest relaxation problems

Ion-electron-radiation equilibration

Ion-electron

equilibration

rage and flash show differences in multigroup tests
RAGE and FLASH show differences in multigroup tests

8 energy groups – constant but different opacity in each group

Significant differences in energy density in each group Smaller differences in temperatures

Differences not yet understood

Comparison with future CRASH results may help track down differences

diffusion tests
Diffusion tests
  • Electron conduction
  • Electron conduction + ion/electron equilibration
  • Gray radiation diffusion
  • Electron conduction + ion/electron equilibration + gray radiation diffusion
  • Electron conduction + ion/electron equilibration + multigroup radiation diffusion
  • Tests run with and without flux limiters
electron conduction test led to discovery of bug in flash
Electron conduction test led to discovery of bug in FLASH

Initial temperature profile

t = 1.5 ns

t = 1.5 ns

Before bug fix in FLASH

After bug fix in FLASH

codes agree on diffusion tests 2 and 3
Codes agree on diffusion tests 2) and 3)

t = 1.5 ns

t = 2.e-5 ns

Conduction + ion/electron coupling

Gray radiation diffusion

All three codes give identical results

codes still agree with full physics
Codes still agree with “full physics”

t = 0.2 ns

Gray diffusion, emission/absorption, electron conduction, electron/ion coupling

hydrodynamics tests not yet completed
Hydrodynamics tests – not yet completed
  • Hydrodynamics (shifted 1d simulations)
    • Hydro + ion/electron equilibration
    • Hydro + electron conduction
    • Hydro + radiation diffusion + electron conduction
we have learned a great deal from these simple test problems
We have learned a great deal from these simple test problems
  • As a result of these tests we were able to
    • Understand some of the differences in the codes more clearly
    • Find bugs in codes
    • Improve the physics models within the codes
    • Test physics that is difficult to verify using analytic solutions
    • Understand time step size requirements for each type of physics
xe opacity comparisons
Xe opacity comparisons

T = 50 eV, r=0.011 gm/cm3

Data plotted for a single matter temperature and density relevant to the CRASH experiment

Relevant photon energies are those below ~300 eV.

magnified view of relevant region
Magnified view of relevant region

T = 50 eV, r=0.011 gm/cm3

shock morphology is sensitive to xe opacity
Shock morphology is sensitive to Xe opacity

Simulations used SESAME gray opacities

Xeopacities multiplied by constant scale factor of 1, 10, and 100

For future studies, different scale factors may

be used for each energy group

more complex comparisons
More complex comparisons
  • Two-dimensional shifted simulations with X-ray drive
  • Two-dimensional simulations of full CRASH experiment with X-ray drive
  • Two-dimensional simulations of full CRASH experiment with input from H2D with laser drive
  • Two-dimensional simulations of full CRASH experiment with self-contained laser drive
tuning crash with x ray drive can eliminate axis feature
Tuning CRASH with X-ray drive caneliminate axis feature

These two simulations are identical except for the temperature of the X-ray drive

initial untuned flash simulation with x ray drive produces the anomalous axis feature
Initial untuned FLASH simulation with X-ray drive produces the anomalous axis feature

Initiated with mono-energetic X-ray drive

Time = 6 ns

low grid resolution can produce misleading results
Low grid resolution can producemisleading results

CASSIO

CASSIO initiated with X-ray drive (mono-energetic photons)

No protruding axis feature at low resolution

high resolution untuned cassio simulation with imc transport produces axis feature
High-resolution untuned CASSIO simulationwith IMC transport produces axis feature

Initiated with X-ray drive (mono-energetic photons)

time = 15 ns

High resolution – 1.5 micron

Protruding feature on axis is present

low resolution hydra simulation with laser drive produces a small axis feature
Low resolution HYDRA simulation with laser drive producesa small axis feature

30 ns

Higher resolution simulation is neededbefore definitive conclusion can be reached about the axis feature

crash hydrodynamic validation study
CRASH hydrodynamic validation study
  • Jacobs’ Richtmyer-Meshkov instability experiment
    • Instability generated by shock impulsively accelerating an interface between two materials
    • Sinusoidal perturbation of interface – amplitude grows in time
    • Performed in vertical shock tube
    • Materials used were air and SF6 (density ratio ~ 1:5)
    • Shock Mach number = 1.21
    • Shock reflects from end of tube and re-shocks the interface
results at 6 ms before re shock
Results at 6 ms (before re-shock)

128 grid points per wavelength

256 grid points per wavelength

Experiment

Experiment shows more roll up than simulations

summary
Summary
  • Detailed comparisons of five HEDP codes have begun
  • Good agreement on many test problems
  • Discrepancies still exist for some simple test problems
  • Comparisons have already led to the discovery of a number of bugs and code improvements
  • Non-planar primary shock has been seen in simulations of the CRASH experiment at high resolution using four of the codes in the test suite
  • Validation simulations of Richtmyer-Meshkov instabilities produced good agreement with Jacobs’ experiments – especially before re-shock