Energy Density Gradient Estimation for Monte Carlo Methods in Mix Models

A common method to solving coupled radiation-hydrodynamics simulations is to use the Implicit Monte Carlo method as the radiation solve and the BHR-2 mix model for the hydrodynamics solve. This methodology has been shown to be susceptible to the stochastic noise inherent to IMC. This thesis shows why the BHR-2 is susceptible to the noise, and why linear filters are not the best solution to alleviating this susceptibility. A finite element representation is derived to approximate the gradient of the energy density, which is the coupling quantity between the radiation and hydrodynamics solve. Results using this finite element estimator, are presented for two problems of different complexity, and compared to results using a finite difference method to approximate the energy density gradient. The estimator is shown to reduce the variance in the gradient, which would lead to a decrease in the computational cost of IMC/BHR-2 simulations, and increase their robustness to stochastic noise