Numerical passage from radiative heat transfer to nonlinear diffusion models

Radiative heat transfer equations including heat conduction are considered in the small mean free path limit. Rigorous results on the asymptotic procedure leading to the equilibrium diffusion equation for the temperature are given. Moreover, the nonlinear Milne problem describing the boundary layer is investigated and an existence result is proven. An asymptotic preserving scheme for the radiative transfer equations with the diffusion scaling is developed. The scheme is based on the asymptotic analysis. It works uniformly for all ranges of mean free paths. Numerical results for different physical situations are presented.