Very high-order asymptotic-preserving schemes for hyperbolic systems of conservation laws with parabolic degeneracy on unstructured meshes

Florian Blachère (1) , Christophe Chalons (2) , Rodolphe Turpault (3, 4)

1 Gamma3 - Automatic mesh generation and advanced methods
2 LMV - Laboratoire de Mathématiques de Versailles
3 IMB - Institut de Mathématiques de Bordeaux
4 Bordeaux INP - Institut Polytechnique de Bordeaux

In this paper, we consider the numerical approximation of hyperbolic systems of conservation laws with sti source terms and parabolic degeneracy in the asymptotic limit. We are more precisely interested in the design of high-order asymptotic-preserving schemes on unstructured meshes. Our approach is based on a very simple modication of the numerical ux associated with the usual HLL scheme and boils down to a sharp control of the underlying numerical diusion. The strategy allows to capture the correct asymptotic parabolic behavior and to preserve the high-order accuracy also in the asymptotic limit. Numerical experiments are proposed to illustrate these properties.

Mots clés: asymptotic-preserving schemes; diffusion limit; nonlinear hyperbolic systems; high order finite volumes schemes

Domaines: Analyse numérique [math.NA]

Florian Blachère, Christophe Chalons, Rodolphe Turpault. Very high-order asymptotic-preserving schemes for hyperbolic systems of conservation laws with parabolic degeneracy on unstructured meshes. Computers & Mathematics with Applications, 2021, 87, pp.41-49. ⟨10.1016/j.camwa.2021.02.003⟩. ⟨hal-03157500⟩