An improved unified gas kinetic particle method for radiative transfer equations. (March 2021) - Shi, Yi; Sun, Wenjun; Li, Lingxiao; Song, Peng
Highlights: A macroscopic system is applied to accelerate the microscopic Monte Carlo simulation for the TRT equations. The micro and macroscopic solvers are tightly coupled in a consistent way. There is no need to track the emission particles, and the statistical noise is reduced. The method has the asymptotic preserving property both in the free transport and diffusion regimes. Abstract: In this paper, we develop a new unified gas kinetic particle (UGKP) method for thermal radiative transfer equations. This method utilizes a system of macroscopic equations to accelerate the evolution of microscopic transport equations. We employ a finite volume formulation for the macroscopic equation, and a particle-based Monte Carlo solver for the evolution of microscopic equation. In comparison with the previous work [19], the new UGKP method utilizes the solutions of macroscopic equations as the final solutions, while the microscopic solver provides the partial numerical flux of the known particles and the initial distribution function for the multi-scale system. By this approach, there is no need to track the particles from the emission source, and the statistical noise can be greatly reduced in optically thick regions. Moreover, we prove that the new UGKP method has the asymptotic preserving property both in the free transport and the diffusion regimes. Several numerical simulation results are given to show the efficiency and capacity of the new method.