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

Abstract

In this paper, we consider the numerical approximation of hyperbolic systems of conservation laws with stiff 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 modification of the numerical flux associated with the usual HLL scheme and boils down to a sharp control of the underlying numerical diffusion. The strategy allows to capture the correct asymptotic parabolic behaviour and to preserve the high-order accuracy also in the asymptotic limit. Numerical experiments are proposed to illustrate these properties.