An asymptotic preserving unified gas kinetic particle method for radiative transfer equations

Abstract

In this work, we propose a unified gas kinetic particle (UGKP) method for solving the nonlinear thermal radiative transfer equations. The UGKP method is a multiscale method in that the macro and microscopic variables are coupled and updated in a consistent way. It employs a finite volume formulation for the macroscopic variable evolution, and a particle-based Monte Carlo solver for tracking the non-equilibrium transport. The stiff coupling between the radiation and material energy is included and resolved efficiently by the coupled macroscopic equations. Compared with the implicit Monte Carlo (IMC) method, it does not employ the effective scattering events. Moreover, we demonstrate that the UGKP method has the asymptotic preserving property in capturing the diffusion limit in optically thick regions. Numerical simulations show that our method is comparable in computational cost to the IMC method for optically thin problems, and becomes much more efficient for optically thick problems. More importantly, the UGKP method doesn't require the cell size being less than the photon's mean free path and it achieves the highest efficiency in the optically thin and thick regions self-adaptively.