Accurate Asymptotic Preserving Boundary Conditions for Kinetic Equations on Cartesian Grids

A simple second-order scheme on Cartesian grids for kinetic equations is presented, with emphasis on the accurate enforcement of wall boundary conditions on immersed bodies. This approach preserves at the discrete level the asymptotic limit towards Euler equations up to the wall, thus ensuring a smooth transition towards the hydrodynamic regime. We investigate exact, numerical and experimental test cases for the BGK model in order to assess the accuracy of the method.