Abstract
We present an asymptotic preserving method for the radiative transfer equations in the framework of \(P_N\) method. An implicit and explicit numerical scheme is proposed to solve the \(P_N\) system based on the order analysis of the expansion coefficients of the specific intensity, where the order of each expansion coefficient is derived by the Chapman-Enskog method. The coefficients at higher-order are treated explicitly while those at lower-order are treated implicitly in each equation of the \(P_N\) system. Energy inequality is proved for this numerical scheme. Several numerical examples validate the efficiency of this scheme in both optically thick and thin regions.
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