The kinetic scheme for the full-Burnett equations

The present paper concerns two aspects for the Burnett equations. First, we are going to theoretically show the consistency between the traditional Chapman–Enskog expansion and the successive approximation for the BGK equation up to the super-Burnett order. Second, we will design a numerical scheme to efficiently solve the Burnett equations. The current approach is an improvement of the BGK-Burnett scheme [K. Xu, Phys. Fluids 15 (2003) 2077], where the locally constant collision frequency is considered. Based on the Burnett distribution function, a high order time accurate numerical flux is derived by different approaches. The resulting scheme is tested in the problem of normal shock wave and that of force-driven Poiseuille flow.