On Numerical Methods for Plasma 3-T Radiation Diffusion in Two and Three Dimensions

Operator-splitting approaches are often used for plasma 3-T radiation diffusion equations, since many linear solvers could not effectively solve the coupled linear system resulted from plasma 3-T radiation diffusion equations. An approach of operator-splitting is proposed for numerically solving plasma 3-T radiation diffusion equations. To resolve sub-cell structure in mixed cells, interface reconstruction is implemented within any mixed cell. Therefore, the system of 3-T radiation diffusion equations is solved on twoand threedimensional polyhedral meshes. The focus of this paper is on the coupling between radiation and material, the treatment of nonlinearity in the equations, and the discontinuity across cell interfaces in material properties. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes. The treatment is exact for arbitrarily strong discontinuity. The features of the resulting scheme are demonstrated through comparing with more accurate methods and some existing operator-splitting methods for numerical examples. It is demonstrated that the proposed approach is much better than the existing splitting approaches and close to unsplit method.