A robust low diffusive kinetic scheme for the Navier-Stokes/Euler equations

A new kinetic scheme based on the equilibrium flux method (EFM) and modified using Osher intermediate states is proposed. This new scheme called EFMO combines the robustness of the equilibrium flux method and the accuracy of flux-difference splitting schemes. The original EFM scheme is expressed in terms of simple wave decomposition in which only the linearly degenerate subpath is calculated from Osher numerical flux while nonlinear waves are still evaluated from the regular EFM splitting. Owing to its capability of withstanding intense nonlinear waves and yet exactly resolving contact discontinuities, EFMO is particularly well suited for the resolution of the Navier-Stokes equations as demonstrated by a series of severe test cases including the high-speed viscous flow around a cone, a shock-boundary layer interaction problem, a vacuum apparition problem, the hypersonic flow around a circular cylinder at Mach 100, and the forward-facing step at Mach 3. (C) 1997 Academic Press.