preliminary sensitivity studies with crash 3d bruce fryxell crash review october 20, 2009

Preliminary Sensitivity Studies With CRASH 3D

Bruce Fryxell

CRASH ReviewOctober 20, 2009

Description of simulations

• Uniform 3D Cartesian grid• Grid size – 1200 x 240 x 240

– A second set of simulations was performed with a grid size of 600 x 120 x 120 to test grid convergence

• Simplified Physics– Gamma-law equation of state for each material– Gray flux-limited diffusion

• All simulations initialized from Hyades 2D output at 1.3 ns using nominal values of input parameters

Description of simulations

• 64 Three-dimensional simulations performed varying four input parameters– Be gamma (1.4 – 1.6667)– Xe gamma (1.1 – 1.4)– Be opacity scale factor (0.7 - 1.3)– Xe opacity scale factor (0.7 – 1.3)

• Parameter combinations determined from Latin hypercube design

• All other parameters were fixed at their nominal values• Each simulation used ~ 5 hours on 1024 cores of hera• Entire set was completed in approximately 2 weeks

Input parameter correlations (experiment design)

Be Gamma Xe Gamma Be Opacity Xe Opacity




Xe

Op

aci

ty

Be

Op

aci

ty

X

e G

amm

a

Be

Ga

mm

a

Good coverage of input parameter space with relatively few points

Reference solution

Log Rho

X

Y

•Slice through z=0 plane

•Morphology of main shock differs significantly from experiments

•Wall shock appears similar to experiments

Axis feature is robust

Reference Solution

Asymmetric Initial Conditions

Rusanov Solver

log rho

log rho

log rho

Also investigated:•Changing interface treatment

•Varying plastic opacity

•Multigroup diffusion

•2D cylindrical grid

For all tests, axis feature persists

We are now investigating the possibility that the feature results from the Hyades initial conditions

•Inadequate grid resolution

•Inconsistent physics

Sensitivity study of observable features

Main shock locationWall shock angle

Distance between wall and triple point

10 additional quantities were studied, but will not be discussed here, since they can not be measured in the experiments

Output quantities of interest

Main shock location is not very sensitive to variations of input parameters

Range of values fromexperiment

Be Opacity Scale Factor Xe Opacity Scale Factor

Be Gamma Xe Gamma

S

hock

Loc

atio

n

Sho

ck L

ocat

ion

S

hock

Loc

atio

n

Sho

ck L

ocat

ion

This study does not address sensitivity of shock location to these parameters during the first 1.3 ns, prior to the initialization of CRASH

Shock location is not converged at low resolution

Shock location is not converged at low resolution, but error is still less than variation in experiment

High resolution uses the same grid size as the nearly converged 1D solution

Multidimensional simulations may require higher resolution that 1D for convergence


Be Gamma Xe Gamma

S

hock

Loc

atio

n

Sho

ck L

ocat

ion

S

hock

Loc

atio

n

Sho

ck L

ocat

ion

Red – Low resolutionBlue – High resolution

Wall shock angle is correlated only with Xe opacity

Value from experiment is ~ 10° ± 2°

Value from simulations is ~ 6° - 8°

These values were determined in different ways and may not be inconsistent

For future studies, all features will be extracted from radiographs in consistent manner

Correlation between the Xe opacity and the wall shock angle makes physical sense


Be Gamma Xe Gamma

W

all S

hock

Ang

le

Wal

l Sho

ck A

ngle

W

all S

hock

Ang

le

Wal

l Sho

ck A

ngle

Low resolution produces larger wall shock angles


Be Gamma Xe Gamma

W

all S

hock

Ang

le

Wal

l Sho

ck A

ngle

W

all S

hock

Ang

le

Wal

l Sho

ck A

ngle

Red – Low resolutionBlue – High resolution

Triple point location shows weak correlation with Xe Gamma

Value from experiment is ~ 6.7 ± 1 x 10-4 m

Value from simulations is ~ 7 – 10 x 10-4 m


Be Gamma Xe Gamma

Trip

le P

oint

Loc

atio

n

T

riple

Poi

nt L

ocat

ion

Trip

le P

oint

Loc

atio

n

T

riple

Poi

nt L

ocat

ion

Triple point location is not very sensitive to grid resolution

Relative importance – Main shock location

MARS MART

The main source of variation in the shock location is the Xe opacity scale factor. However, the size of the variation is very small. The shock location may be more sensitive to these parameters during the first 1.3 ns, before the initialization of CRASH.

Relative importance – Wall shock angle

MARS MART

Variations in the Xe opacity scale factor produce almost the entire variation in the wall shock angle.

Relative importance –Triple point location

MARS MART

Variations in the Xe gamma produce most of the variation in the wall triple point location.

Conclusions

• Location of main shock, the angle of the wall shock, and the location of the triple point show surprisingly good agreement with the experiments

• However, the morphology of the experimental results differs significantly from the simulations

• These differences appear to be robust for the given set of initial conditions

• Differences are likely due to either insufficient numerical resolution in the 2D Hyades initialization calculation, or inconsistent physics between Hyades and CRASH, which creates a strong transient in the solution

Conclusions

• Location of main shock varies little with changes in Be and Xe equation of state and opacity

• Angle of wall shock depends only on the Xe opacity scale factor

• Location of triple point depends primarily on the Xe equation of state

• All conclusions must be regarded as preliminary until higher-fidelity simulations have been completed

We expect to be cycle limited

• Current study required 2 weeks on hera• A study with twice the resolution on a uniform grid would

require approximately 1 year• The use of AMR will reduce this significantly• Future studies may require hundreds rather than tens of

simulations• Use of more sophisticated radiation transport algorithms

will increase computer time dramatically• We intend to make judicious use of two-dimensional and

reduced physics simulations• Two-dimensional simulations will not be possible for

simulations of year five experiments• Completing the project given the computer resources

currently available will be a challenge

Sample flow morphologies

preliminary sensitivity studies with crash 3d bruce fryxell crash review october 20, 2009

Documents

gamma xe gamma slide

xe opacity value

low resolution shock

experiments wall shock

sensitivity of shock

initialization of crash

d cartesian grid grid

d cylindrical grid