The goal of the Center for Radiative Shock Hydrodynamics (CRASH) is to develop and demonstrate methods for the Assessment of Predictive Capability (APC) of complex computer simulations, by working with simulations of radiative shock experiments performed on high-energy laser systems. The radiative shocks are driven in xenon gas by a Be plasma accelerated to > 150 km/s by laser ablation. Figure 1 shows the base geometry. The simulations are based on adding capability to two codes: the Block-Adaptive Tree, Solar-wind Roe-type Upwind Scheme (BATSRUS) code used extensively in space weather modeling by the University of Michigan (UM), and the Parallel Deterministic Transport (PDT) code developed initially for neutron transport calculations on massively parallel computers by Texas A&M University (TAMU).
Physical Experiments and Predictions
We have also now conducted two experimental sequences. The first was aimed at quantifying experimental variability in our base radiative shock system. The second was aimed at calibrating the early-time behavior of our experimental system, by measuring the emergence of the shock wave from the laser-driven Be disk.
We are designing our next experiments with substantial input from our predictive capability analysis. In August 2010, we will measure the shock structure at 26 ns, much later than in our previous experiments which were primarily near 13 ns. We are now predicting the probability distribution of the outcomes of this experiment using the CRASH 2.0 code and a Bayesian calibration employing all the previous data. In designing the December 2010 experiments, we are assessing the utility for validation of several possible experiments. We will then proceed to predict the outcome of this experiment in advance of its execution. We anticipate undertaking a similar process for at least one more experiment before predicting and then shooting the year-5 experiment shown in Figure 1.
CRASH 2.0 includes a TVD MUSCL hydrodynamic capability, multigroup-diffusion radiation transport, dynamic adaptive mesh refinement, and electron physics including heat transport, level sets to track material boundaries, first-principles-based equation of state and opacity models, and the ability to work in XYZ or RZ geometry. This completes the minimum set of physics that we expect may be needed to model our physical system.
Goals and Methods for Prediction
The goal is for the predictive capability of the simulation to be comparable to the experimental variabilities, which are approximately 10%. The assessment of predictive capability includes:
- physically motivated tests and statistical sensitivity studies using space-filling, Latin-hypercube designs, supported by Bayesian MARS, MART, and Gaussian process analyses,
- physically motivated statistical emulation of simulated initial conditions,
- space-filling, Latin-hypercube sets of simulation runs,
- post-processing of these simulation runs to extract measured parameters,
- Bayesian, Gaussian-process-model analysis of the output and of the measured data to determine posterior probability distributions of physical input parameters.