Asymptotic preserving schemes on distorted meshes for Friedrichs systems with sti relaxation: application to angular models in linear transport

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 di usive regime. For the hyperbolic heat equation we use asymptotic preserving schemes recently designed previously. To discretize the second part we use classical Rusanov or upwind schemes. To nish we apply this method for the discretization of the PN and SN models which are widely used in transport codes.

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