An asymptotic-preserving scheme for systems of conservation laws with source terms on 2D unstructured meshes

Abstract

In this paper, finite volume numerical schemes are developed for hyperbolic systems of conservation laws with source terms. The systems under consideration degenerate into parabolic systems in large times when the source terms become stiff. In this framework, it is crucial that the numerical schemes are asymptotic-preserving, i.e., that they degenerate accordingly. Here, an asymptotic-preserving numerical scheme is proposed for any system within the aforementioned class on 2D unstructured meshes.

This scheme is proved to be consistent and stable under a suitable CFL condition. Moreover, we show that it is also possible to prove that it preserves the set of (physically) admissible states under a geometric property on the mesh. Finally, numerical examples are given to illustrate its behavior.