An extremum‐preserving finite volume scheme for three‐temperature radiation diffusion equations

Abstract

In this paper, an extremum‐preserving finite volume scheme is constructed for the two‐dimensional three‐temperature (2D 3‐T) radiation diffusion equations. The harmonic averaging points located at cell edge are applied to define the auxiliary unknowns, and the primary unknowns are defined at cell center. This scheme has a fixed stencil and satisfies the local conservation condition and discrete extremum principle. The existence of discrete solution is proved by using the fixed point theorem. Moreover, the stability analysis of this scheme is also presented. Numerical results illustrate that this scheme is efficient and accurate in solving the 2D 3‐T radiation diffusion equations on distorted meshes.