Asymptotic preserving scheme and numerical methods for radiative hydrodynamic models

In this Note, we present a scheme for nonlinear radiative systems which are compatible with diffusive asymptotics. The scheme is based on a splitting: firstly we use a relaxation step to change the problem into 2 identical systems of linear transport systems and, secondly, we use a so-called 'well balanced' scheme for each of the 2 systems. The main advantages of our scheme is that it is fully implicit and compatible with physical properties (positivity); it can be used with a nonconstant cross section and for nonuniform mesh. (C) 2004 Published by Elsevier SAS on behalf of Academie des sciences.