An inverse Lax-Wendroff method for boundary conditions applied to Boltzmann type models

Francis Filbet (1) , Chang Yang (1, 2)

1 ICJ - Institut Camille Jordan
2 LPP - Laboratoire Paul Painlevé - UMR 8524

In this paper we present a new algorithm based on Cartesian meshes for the numerical approximation of kinetic models set in an arbitrary geometry. Due to the high dimensional property of kinetic models, numerical algorithms based on unstructured meshes are not really appropriate since most of numerical methods (semi-Lagrangian, spectral methods) are particularly efficient on structured grids. Here we propose to adapt the inverse Lax-Wendroff procedure, which has been recently introduced for conservation laws [21], for kinetic equations. Numerical simulations in 1D x 3D and 2D x 3D based on this approach are proposed for Boltzmann type operators (BGK, ES-BGK models).

Mots clés: Inverse Lax-Wendroff procedure; WENO; Boltzmann type models

Domaines: Analyse numérique [math.NA]

Francis Filbet, Chang Yang. An inverse Lax-Wendroff method for boundary conditions applied to Boltzmann type models. Journal of Computational Physics, 2013, 245, pp.43-61. ⟨hal-00732107⟩