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Page 2
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
Page 3
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
Page 4
Input parameter correlations (experiment design)
Be Gamma Xe Gamma Be Opacity Xe Opacity
Be Gamma Xe Gamma Be Opacity Xe Opacity
Be Gamma Xe Gamma Be Opacity Xe Opacity
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
Page 5
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
Page 6
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
Page 7
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
Page 8
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
Page 9
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 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
Red – Low resolutionBlue – High resolution
Page 10
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 Opacity Scale Factor Xe Opacity Scale Factor
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
Page 11
Low resolution produces larger wall shock angles
Be Opacity Scale Factor Xe Opacity Scale Factor
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
Page 12
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 Opacity Scale Factor Xe Opacity Scale Factor
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
Page 13
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.
Page 14
Relative importance – Wall shock angle
MARS MART
Variations in the Xe opacity scale factor produce almost the entire variation in the wall shock angle.
Page 15
Relative importance –Triple point location
MARS MART
Variations in the Xe gamma produce most of the variation in the wall triple point location.
Page 16
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
Page 17
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
Page 18
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