An asymptotic-preserving IMEX PN method for the gray model of the radiative transfer equation

TL;DR

This paper introduces an asymptotic-preserving IMEX PN numerical scheme for the gray radiative transfer equation, ensuring stability and efficiency across different regimes, validated through theoretical proofs and benchmark tests.

Contribution

It presents a novel AP IMEX PN method for the gray radiative transfer model, with proven stability and applicability to both linear and nonlinear cases.

Findings

The scheme is asymptotic-preserving both theoretically and numerically.

Numerical stability is confirmed via Fourier analysis.

Benchmark tests demonstrate the scheme's efficiency.

Abstract

An asymptotic-preserving (AP) implicit-explicit PN numerical scheme is proposed for the gray model of the radiative transfer equation, where the first- and second-order numerical schemes are discussed for both the linear and nonlinear models. The AP property of this numerical scheme is proved theoretically and numerically, while the numerical stability of the linear model is verified by Fourier analysis. Several classical benchmark examples are studied to validate the efficiency of this numerical scheme.