An Asymptotic-Preserving Hybrid Angular Discretization for the Gray Radiative Transfer Equations

The aim of this paper is to construct a new numerical scheme for the nonlinear gray radiative transfer (GRT) equations, namely, the asymptotic-preserving (AP) HNT-based unified gas kinetic scheme (UGKS). The constructed scheme is obtained by combing the UGKS for spatial discretization with the hybrid HNT method for angular discretization. Since the HNT is a hybrid angular discrete method of both PN and SN methods, the current HNT-based UGKS can not only mitigate the ray effects of the SN method largely, but also suppress the oscillations of the original PN method. Furthermore, we show that the current HNT-based UGKS also inherits the AP property of UGKS. A number of one-dimensional and two-dimensional numerical experiments are presented that validate the performance of the current scheme in both optically thin and thick regimes, as well as in mitigating the ray effects. Moreover, it can capture the initial layer solution without requiring additional treatments.