Asymptotic-Preserving Discrete Schemes for Non-Equilibrium Radiation Diffusion Problem in Spherical and Cylindrical Symmetrical Geometries (Communications in Computational Physics, 2018)
We study the asymptotic-preserving fully discrete schemes for non-equilibriumradiation diffusion problem in spherical and cylindrical symmetric geometry.The research is based on two-temperature models with Larsen's flux-limiteddiffusion operators. Finite volume spatially discrete schemes are developed to circumventthe singularity at the origin and the polar axis and assure local conservation.Asymmetric second order accurate spatial approximation is utilized instead ofthe traditional first order one for boundary flux-limiters to consummate the schemeswith higher order global consistency errors. The harmonic average approach in sphericalgeometry is analyzed, and its second order accuracy is demonstrated. By formalanalysis, we prove these schemes and their corresponding fully discrete schemes withimplicitly balanced and linearly implicit time evolutions have first order asymptotic-preservingproperties. By designing associated manufactured solutions and referencesolutions, we verify the desired performance of the fully discrete schemes with numericaltests, which illustrates quantitatively they are first order asymptotic-preservingand basically second order accurate, hence competent for simulations of both equilibriumand non-equilibrium radiation diffusion problems.