An asymptotic-preserving IMEX method for nonlinear radiative transfer equation

TL;DR

This paper introduces an asymptotic-preserving IMEX numerical scheme for nonlinear radiative transfer equations using the PN method, effectively handling both optically thick and thin regimes.

Contribution

The paper develops a novel IMEX scheme that combines implicit and explicit treatments based on coefficient order analysis, ensuring asymptotic preservation for radiative transfer.

Findings

The scheme is validated through numerical examples in various regimes.

Energy inequality is proved for the proposed numerical method.

The method effectively handles stiff and non-stiff parts of the equations.

Abstract

We present an asymptotic preserving method for the radiative transfer equations in the framework of PN method. An implicit and explicit method is proposed to solve the P N system based on the order analysis of the expansion coefficients of the distribution function. The order of each coefficient expanded in the Knudsen number is found through the process of Maxwellian iteration, and the coefficients of high order are treated explicitly while that of low order are treated implicitly in each equation of P N system. Energy inequality is proved for this numerical scheme. Several numerical examples validate this new AP scheme in both optical thick and thin regions.