Implicit Monte Carlo (IMC) and Implicit Monte Carlo Diffusion (IMD) are approaches to the numerical solution of the equations of radiative transfer. IMD was previously derived and numerically tested on grey, or frequency-integrated problems [1]. In this research, we extend Implicit Monte Carlo Diffusion (IMD) to account for frequency dependence, and we implement the difference formulation [2] as a source manipulation variance reduction technique. We derive the relevant probability distributions and present the frequency dependent IMD algorithm, with and without the difference formulation. The IMD code with and without the difference formulation was tested using both grey and frequency dependent benchmark problems. The Su and Olson semi-analytic Marshak wave benchmark was used to demonstrate the validity of the code for grey problems [3]. The Su and Olson semi-analytic picket fence benchmark was used for the frequency dependent problems [4]. The frequency dependent IMD algorithm reproduces the results of both Su and Olson benchmark problems. Frequency group ref nement studies indicate that the computational cost of ref ning the group structure is likely less than that of group ref nement in deterministic solutions of the radiation diffusion methods. Our results show that applying the difference formulation to the IMD algorithm can result in an overall increase in the f gure of merit for frequency dependent problems. However, the creation of negatively weighted particles from the difference formulation can cause signif cant numerical instabilities in regions of the problem with sharp spatial gradients in the solution. An adaptive implementation of the difference formulation may be necessary to focus its use in regions that are at or near thermal equilibrium.
This work describes how to couple a hybrid Implicit Monte Carlo Diffusion (HIMCD) method with a Lagrangian hydrodynamics code to evaluate the coupled radiation hydrodynamics equations. This HIMCD method dynamically applies Implicit Monte Carlo Diffusion (IMD) [1] to regions of a problem that are opaque and diffusive while applying standard Implicit Monte Carlo (IMC) [2] to regions where the diffusion approximation is invalid. We show that this method significantly improves the computational efficiency as compared to a standard IMC/Hydrodynamics solver, when optically thick diffusive material is present, while maintaining accuracy. Two test cases are used to demonstrate the accuracy and performance of HIMCD as compared to IMC and IMD. The first is the Lowrie semi-analytic diffusive shock [3]. The second is a simple test case where the source radiation streams through optically thin material and heats a thick diffusive region of material causing it to rapidly expand. We found that HIMCD proves to be accurate, robust, and computationally efficient for these test problems.
In this work, we introduce a modified Implicit Monte Carlo (IMC) Random Walk (RW) algorithm, which increases simulation efficiency for multigroup radiative transfer problems with strongly frequency-dependent opacities.To date, the RW method has only been implemented in "fully-gray" form;
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