A $H^T_N$-Based UGKS Scheme for the Three-Temperature Radiative Transfer Equations (Communications in Computational Physics, 2025)
The aim of this paper is to propose an asymptotic preserving numericalscheme for the three-temperature radiative transfer equations, which couple the radiative transfer equation with the electron and ion diffusive equations. The $H^T_N$ methodis used for angular discretization, and the unified gas kinetic scheme (UGKS) is usedfor spatial discretization to obtain the asymptotic preserving property of the proposedscheme. Since it includes the electron-ion heat conduction, radiation-electron couplingand electron-ion coupling terms, the three-temperature model exhibits strong nonlinearity and strong coupling properties. By carefully dealing with these coupling termsimplicitly and using an iteration method to solve the electron-ion diffusive system, wecan adapt the $H^T_N$-based UGKS method for the grey radiative transfer equations to dealwith this complex model. According to the asymptotic preserving property of the proposed scheme, it is not necessary in optically thick regimes to restrict the spatial stepsize smaller than the photon mean free path in order to approximate the solution ofthe three-temperature, two-temperature, and single-temperature diffusion limit equations under difference circumstances. The robustness and effectiveness of the currentscheme are verified by several numerical experiments.