A monotone diffusion scheme for 3D general meshes: Application to radiation hydrodynamics in the equilibrium diffusion limit

We propose in this article a monotone finite volume diffusion scheme on 3D general meshes for the radiation hydrodynamics. Primary unknowns are averaged value over the cells of the mesh. It requires the evaluation of intermediate unknowns located at the vertices of the mesh. These vertex unknowns are computed using an interpolation method. In a second step, the scheme is made monotone by combining the computed fluxes. It allows to recover monotonicity, while making the scheme nonlinear. This scheme is inserted into a radiation hydrodynamics solver and assessed on radiation shock solutions on deformed meshes.