Numerical boundary conditions in Finite Volume and Discontinuous Galerkin schemes for the simulation of rarefied flows along solid boundaries

Céline Baranger; Nicolas Hérouard; Julien Mathiaud; Luc Mieussens

doi:10.1016/j.matcom.2018.11.011

paper

Numerical boundary conditions in Finite Volume and Discontinuous Galerkin schemes for the simulation of rarefied flows along solid boundaries

arXiv:2003.05677 · doi:10.1016/j.matcom.2018.11.011

Abstract

We present a numerical comparison between two standard finite volume schemes and a discontinuous Galerkin method applied to the BGK equation of rarefied gas dynamics. We pay a particular attention to the numerical boundary conditions in order to preserve the rate of convergence of the method. Most of our analysis relies on a 1D problem (Couette flow), but we also present some results for a 2D aerodynamical flow.