Asymptotic-preserving discrete unified gas-kinetic scheme for nonlinear gray radiative transfer equations.

Abstract

The solution of the nonlinear gray radiative transfer system composed of the radiative transfer equation (RTE) and the material energy balance equation encounters significant challenges in multiscale problems where both optical thick and optical thin regions coexist. In this paper, an asymptotic-preserving (AP) scheme based on the discrete unified gas-kinetic scheme (DUGKS) framework is proposed. The microscopic RTE is solved by a simplified DUGKS, where the cell interface intensity is simply constructed from the averaging along the characteristic line, and the macroscopic material energy balance equation is solved by a finite volume method consistent with the DUGKS. The time marching of the present method exhibits the implicit characteristic, and the mesh size is not strictly constrained by the photon mean free path. As a result, the present method has the AP property. Theoretical analysis is conducted to prove the AP property, and several single- and multiscale tests are carried out to confirm the accuracy and robustness of the present method.