An Efficient WENO-reconstruction-based high-order Gas-kinetic Scheme for Viscous Flows

Based on the Weighted Essential Non-Oscillatory (WENO) reconstruction for the macroscopic flow variables and the direct use of the corresponding gas distribution function of the NavierStokes (NS) solution, a high-order finite volume gas-kinetic scheme is constructed. Different from the previous high-order gas-kinetic method [Li, Xu, and Fu, A high-order gas-kinetic Navier-Stokes solver, J. Comput. Phys., 229 (2010) 6715-6731], which uses a discontinuous initial reconstruction at the cell interface, the present scheme is based on a continuous flow distribution. In the current study, in order to capture the discontinuities properly, the WENO reconstruction is combined with monotonicity preserving limiter in the initial data reconstruction. The space and time dependent multidimensional NS gas distribution function is used to evaluate the time-dependent interface flux function, which is further integrated along the cell boundary to get total mass, momentum, and energy transport within a time step. Since the Runge-Kutta time stepping method is not used here, the current scheme becomes highly accurate and efficient. With the same WENO reconstruction on characteristic variables, the current multidimensional finite volume gas-kinetic scheme is even more accurate and efficient than the well-defined finite difference WENO-JS scheme [Jiang and Shu, Efficient implementation of Weighted ENO schemes, J. Comput. Phys. 126 (1996) 202-228]. The numerical experiments also show that the current scheme is highly stable and non-oscillatory in capturing discontinuity.