Inverse Lax-Wendroff method for boundary conditions of Boltzmann type models

TL;DR

This paper introduces an inverse Lax-Wendroff method on Cartesian meshes for accurately imposing boundary conditions in high-dimensional kinetic models like Boltzmann equations, improving computational efficiency on complex geometries.

Contribution

The paper extends the inverse Lax-Wendroff procedure to kinetic equations, enabling boundary condition implementation on Cartesian grids for complex geometries in Boltzmann models.

Findings

The algorithm accurately approximates boundary conditions for Boltzmann models.

Numerical results demonstrate the method's high accuracy.

Applications in 1Dx3D and 2Dx3D show effectiveness.

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.