tion law form. A unique Maxwellian distribution is then constructed from the updated physical values of each cell A new kinetic scheme based on the equilibrium flux method (EFM) and modified using Osher intermediate states is proposed. This and the process repeats.
new scheme called EFMO combines the robustness of the equilib-Among its mathematical properties, EFM has been forrium flux method and the accuracy of flux-difference splitting mally shown to be entropy satisfying [5] and positivity schemes. The original EFM scheme is expressed in terms of simple preserving [6]. Furthermore, Macrossan [7] has pointed wave decomposition in which only the linearly degenerate subpath out the upwinding mechanism of EFM by proving that its is calculated from Osher numerical flux while nonlinear waves are numerical dissipation vanishes when the Mach number still evaluated from the regular EFM splitting. Owing to its capability of withstanding intense nonlinear waves and yet exactly resolving increases. For moderate values of the Mach number, howcontact discontinuities, EFMO is particularly well suited for the resoever, EFM suffers from an excessive numerical diffusion lution of the Navier-Stokes equations as demonstrated by a series that can dramatically smear out contact discontinuities. of severe test cases including the high-speed viscous flow around An alternative approach developed independently by a cone, a shock-boundary layer interaction problem, a vacuum appa-Macrossan [8] and Xu [9] consists of directly reconstructing rition problem, the hypersonic flow around a circular cylinder at Mach 100, and the forward-facing step at Mach 3. ᮊ 1997 Academic the conservative variables at the interface from the contri-Press bution of two half-Maxwellians associated with the physical states on either sides of the interface. The resulting scheme is very low diffusive and performs well for boundary layer 193