Preliminary Sensitivity Studies With CRASH 3D Bruce Fryxell CRASH Review October 20, 2009

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 – ) –Xe gamma (1.1 – 1.4) –Be opacity scale factor ( ) –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 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 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 location Wall 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 from experiment Be Opacity Scale Factor Xe Opacity Scale Factor Be Gamma Xe Gamma 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 Red – Low resolution Blue – 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

Page 11 Low resolution produces larger wall shock angles Be Opacity Scale Factor Xe Opacity Scale Factor Be Gamma Xe Gamma Red – Low resolution Blue – High resolution

Page 12 Triple point location shows weak correlation with Xe Gamma Value from experiment is ~ 6.7 ± 1 x m Value from simulations is ~ 7 – 10 x m Be Opacity Scale Factor Xe Opacity Scale Factor Be Gamma Xe Gamma 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

Page 19 Sample flow morphologies