Moving mesh finite difference solution of non-equilibrium radiation diffusion equations

TL;DR

This paper introduces a moving mesh finite difference method for solving complex non-equilibrium radiation diffusion equations, effectively capturing wave profiles and local structures with improved efficiency and solution positivity.

Contribution

It proposes a novel moving mesh finite difference approach with a predictor-corrector scheme and cutoff strategy to handle nonlinear diffusion and maintain positivity in non-equilibrium radiation diffusion models.

Findings

Method accurately captures Marshak wave profiles

Adaptive moving meshes outperform uniform meshes

Solutions agree well with existing literature

Abstract

A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves nonlinear diffusion coefficients and its solutions stay positive for all time when they are positive initially. Nonlinear diffusion and preservation of solution positivity pose challenges in the numerical solution of the model. A coefficient-freezing predictor-corrector method is used for nonlinear diffusion while a cutoff strategy with a positive threshold is used to keep the solutions positive. Furthermore, a two-level moving mesh strategy and a sparse matrix solver are used to improve the efficiency of the computation. Numerical results for a selection of examples of multi-material non-equilibrium radiation diffusion show that the method is capable of capturing the profiles and local structures of Marshak waves with adequate mesh concentration. The obtained numerical solutions are in good agreement with those in the existing literature. Comparison studies are also made between uniform and adaptive moving meshes and between one-level and two-level moving meshes.