Flux-difference splitting-based upwind compact schemes for the incompressible Navier-Stokes equations

Third-order and fifth-order upwind compact finite difference schemes based on flux-difference splitting are proposed for solving the incompressible Navier-Stokes equations in conjunction with the artificial compressibility (AC) method. Since the governing equations in the AC method are hyperbolic, fluxdifference splitting (FDS) originally developed for the compressible Euler equations can be used. In the present upwind compact schemes, the split derivatives for the convective terms at grid points are linked to the differences of split fluxes between neighboring grid points, and these differences are computed by using FDS. The viscous terms are approximated with a sixth-order central compact scheme. Comparisons with 2D benchmark solutions demonstrate that the present compact schemes are simple, efficient, and high-order accurate.