The present work concerns the numerical approximation of the M1model for radiative transfer. The main purpose is to introduce an accurate finite
volume method according to the nonlinear system of conservation laws that governs
this model. We propose to derive an HLLC method which preserves the stationary
contact waves. To supplement this essential property, the method is proved
to be robust and to preserve the physical admissible states. Next, a relevant asymptotic
preserving correction is proposed in order to obtain a method which is able
to deal with all the physical regimes. The relevance of the numerical procedure is
exhibited thanks to numerical simulations of physical interest.