Asymptotic Preserving Schemes on Distorted Meshes for Friedrichs Systems with Stiff Relaxation: Application to Angular Models in Linear Transport

Abstract

In this paper we propose an asymptotic preserving scheme for a family of Friedrichs systems on unstructured meshes based on a decomposition between the hyperbolic heat equation and a linear hyperbolic which not involved in the diffusive regime. For the hyperbolic heat equation we use asymptotic preserving schemes recently designed in [7]---[20]. To discretize the second part we use classical Rusanov or upwind schemes. To finish we apply this method for the discretization of the $$P_N$$ P N and $$S_N$$ S N models which are widely used in transport codes.