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 con- ditions 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.