A Finite Volume Scheme Preserving Maximum Principle for the System of Radiation Diffusion Equations with Three-Temperature.

We propose a cell-centered nonlinear finite volume scheme for the nonequilibrium three-temperature equations, where both the Dirichlet and Neumann boundary conditions are considered, and prove that the discrete solutions of the scheme satisfy the discrete maximum principle. In the construction of the flux we use the nonlinear combination of two single fluxes and the interpolation technique for the auxiliary unknowns. Some new interpolation methods are introduced, especially when the Neumann boundary condition is considered. Based on the bounded estimation of the discrete solution, we prove that there exists at least a solution for our scheme by using the Brouwer's fixed point theorem. Numerical results show that our scheme has second-order accuracy and good conservation and can preserve the discrete maximum principle.