Monotone Finite Volume Schemes of Nonequilibrium Radiation Diffusion Equations on Distorted Meshes

Abstract

We construct a monotone finite volume scheme on distorted meshes for multimaterial, nonequilibrium radiation diffusion problems, which are described by the coupled radiation diffusion and material conduction equations. Moreover, we prove theoretically that the scheme is monotone. Numerical results are presented to show that our scheme preserves positivity of solution on various distorted meshes, and the contours of numerical solution obtained by our scheme on distorted meshes accord with that on rectangular meshes. Moreover, numerical tests indicate that our monotone scheme is more computationally efficient than the nine point scheme. These results show that our nonlinear monotone finite volume scheme is a practical and attractive method for solving nonlinear diffusion equations on distorted meshes.