Simple Corner Balance Method for Transport in Radiation Hydrodynamics Calculations

Simple Corner Balance (SCB) spatial discretization is feasible for solving transport equations on quadrilateral grids. We generalize it for nonlinear radiative transfer equations in the system of radiative hydrodynamics. As four radiation unknowns are defined in four subcells of a cell, how to discretize electronic temperature while radiation and mather are strong coupled via absorption and emission. In this paper, subcell-cell lax coupling way and subcell-subcell tight coupling way are considered. Numerical tests demonstrate in subcell-subcell tight coupling way meshes are only required sufficiently fine to resolve the transport processes on the coarser length-scale associated with the diffusion of radiation energy through opaque media, other than required to resolve down to a photon mean free path in subcell-cell lax coupling way.