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

TL;DR

This paper introduces an asymptotic preserving numerical scheme for Friedrichs systems on distorted meshes, effectively handling the diffusive limit and applied to angular models in linear transport.

Contribution

It develops a novel scheme combining hyperbolic heat equation discretization with classical methods, suitable for unstructured meshes and transport models.

Findings

Effective handling of diffusive limit in Friedrichs systems

Applicable to PN and SN transport models

Uses a combination of recent asymptotic preserving schemes and classical discretizations

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 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.