An efficient high-order finite difference gas-kinetic scheme for the Euler and Navier-Stokes equations

摘要

Based on the temporal evolution of the Navier-Stokes gas distribution function and Weighted Essential Non-Oscillatory (WENO) interpolation, a high-order finite difference gas-kinetic scheme (FDGKS) is constructed. Different from the previous high-order finite volume gas-kinetic method [Li, Xu, and Fu, J. Corn put. Phys. vol. 229, pp. 6715 (2010)], which uses a discontinuous initial reconstruction at the cell interface, the present scheme is a finite-difference one with a continuous flow distribution at the grid point.