Asymptotic preserving discretisation of a Jin–Xin model with implicit equilibrium manifold on a bounded domain

Nicolas Seguin (1) , Magali Tournus (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 ECM - École Centrale de Marseille

In this paper, we design and analyze a numerical scheme which approximates a Jin–Xin linear system with implicit equilibrium on a bounded domain. This scheme relaxes toward the asymptotic limit of the linear system. The main properties of the limiting scheme are that it does no require to invert the implicit function defining the manifold, and that it provides an accurate discretization of the boundary conditions.

Mots clés: Hyperbolic Relaxation; Asymptotic Preserving scheme; Boundary layer

Domaines: Mathématiques [math]

Nicolas Seguin, Magali Tournus. Asymptotic preserving discretisation of a Jin–Xin model with implicit equilibrium manifold on a bounded domain. IMA Journal of Numerical Analysis, 2020, 40 (1), pp.530-562. ⟨10.1093/imanum/dry089⟩. ⟨hal-01819256⟩