An AUSM-based high-order compact method for solving Navier-Stokes equations

A high-order compact upwind algorithm is developed for solving Navier-Stokes equations in two-space dimensions. The method is based on advection upstream splitting method and fourth-order compact finite-difference schemes. The convection flux terms of the Navier-Stokes equations are discretized by a compact cell-centered differencing scheme while the diffusion flux terms are discretized by a central fourth-order compact scheme. The midpoint values of the flux functions required by the cell-centered compact scheme are determined by a fourth-order MUSCL approach. For steady-state solutions; first-order implicit time integration, with LU decomposition, is employed. Computed results for a laminar flow past a flat plate and the problem of shock-wave boundary layer interaction are presented.