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

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 1 D × 3 D and 2 D × 3 D based on this approach are proposed for Boltzmann type operators (BGK, ES-BGK models).