An asymptotic preserving unified gas kinetic particle method for a three-temperature radiative transfer model

In this work, we propose an efficient Monte Carlo method for the simulation of the coupled three-temperature thermal radiative transfer problems. Our method is based on the unified gas kinetic particle method, which has been previously developed for the two-temperature radiative transfer equations. This method is a multiscale method in that the macro- and microscopic variables are coupled and updated in a consistent way. For the three-temperature system of macroscopic evolution equations, it is solved by the finite volume discretization method, and an efficient iterative method is proposed for the nonlinear system. By this method, the coupling terms between the electron, ion and radiation are treated simultaneously. For the microscopic equation of radiation intensity, it is solved by the particle-based Monte Carlo method. The solutions of macroscopic equations provide the emission source for the microscopic Monte Carlo solver. Moreover, we demonstrate that the proposed method can capture the asymptotic property of two limiting models: the equilibrium diffusion limit equation when the opacity tends to infinity and the two-temperature transport limit equation when the ion-electron coupling coefficient tends to infinity. Numerical experiments are given to show the performance and effectiveness of the proposed method.