An efficient asymptotic preserving Monte Carlo method for radiative transfer equations

Abstract

In this work, an efficient asymptotic preserving Monte Carlo method is developed for nonlinear thermal radiative transfer equations. We derive a new approximate macroscopic equation for the radiation energy density, from an integral solution of the radiation intensity along characteristics of the microscopic equation. We will solve a coupled macro-micro system with a hybrid numerical method. The macroscopic radiation and material energy densities are updated first by using a deterministic finite volume method. The microscopic equation, with the emission source provided from the macroscopic variables, can then be efficiently solved using a particle-based Monte Carlo method. This new approach is uniformly stable, with large time steps independent of scaling parameters and the speed of light. Besides, it can be shown that the method is asymptotic preserving in the diffusive limit for an optically thick regime. Numerical experiments are performed to demonstrate the high efficiency and good performances of our proposed method.