An asymptotic preserving scheme with the maximum principle for the [formula omitted] model on distorded meshes

Abstract

In this Note, we show that a recent scheme introduced by Buet et al. (2011) [5] for the nonlinear two moments M1 model of linear transport and which captures correctly the diffusion limit on distorded meshes (AP scheme) also possesses the maximum principle. The main idea of the design of this scheme is to rewrite the model as a gas dynamics model and to use an Eulerian scheme, derived from a Lagrange + remap scheme. To obtain the AP property we use the multidimensional extension, developed by Buet et al. (2012) [6], of the Jin and Levermore (1996) procedure [9] for the hyperbolic heat equation. We will show that this scheme is entropic which ensures the maximum principle of the M1 model. More we present some numerical results, on distorted quadrangular and triangular meshes which show that the scheme is second order in the diffusive regime.