Asymptotic-preserving &; well-balanced schemes for radiative transfer and the Rosseland approximation

Summary. We are concerned with efficient numerical simulation of the radiative transfer equations. To this end, we follow the Well-Balanced approachs canvas and reformulate the relaxation term as a nonconservative product regularized by steady-state curves while keeping the velocity variable continuous. These steady-state equations are of Fredholm type. The resulting upwind schemes are proved to be stable under a reasonable parabolic CFL condition of the type tO(x²) among other desirable properties. Some numerical results demonstrate the realizability and the efficiency of this process.Mathematics Subject Classification (1991): 82C70, 65M06, 35B25Work partially supported by EEC network #HPRN-CT-2002-00282.Revised version received July 21, 2003