Design of asymptotic preserving finite volume schemes for the hyperbolic heat equation on unstructured meshes

Abstract

We propose an asymptotic preserving nodal discretization of the hyperbolic heat equation, also known as the P 1 equation, on unstructured meshes in 2-D. This method, in diffusive regime, overcomes the problem of the inconsistent limit with diffusion, of classical multidimensional extensions of 1-D asymptotic preserving schemes, based on edge formulation. We provide both theoretical and numerical results.