Inverse Lax-Wendroff method for boundary conditions of Boltzmann type models
arXiv:1209.3103 · doi:10.1016/j.jcp.2013.03.015
Abstract
In this paper we present a new algorithm based on a Cartesian mesh for the numerical approximation of kinetic models on complex geometry boundary. Due to the high dimensional property, numerical algorithms based on unstructured meshes for a complex geometry are not appropriate. Here we propose to develop an inverse Lax-Wendroff pro- cedure, which was recently introduced for conservation laws [S. Tan & C.W. Shu, JCP (2010)], to the kinetic equations. Applications in 1Dx3D and 2Dx3D of this algorithm for Boltzmann type operators (BGK, ES-BGK models) are then presented and numerical results illustrate the accuracy properties of this algorithm.
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