Solution of the parabolized Navier-Stokes equations using Osher's upwind scheme

A new, explicit, finite volume algorithm based on Osher's upwind method is applied to the two-dimensional parabolized Navier-Stokes equations to model hypersonic flows. The algorithm is second-order accurate and employs flux limiters to make the scheme total variation diminishing (TVD). The pressure gradient in the subsonic region is limited in the streamwise direction to maintain a hyperbolic inviscid equation set. Second-order central differencing is applied to the viscous terms and upwind differencing is applied to the inviscid terms in both the subsonic and supersonic portions of the flowfield. The new algorithm is demonstrated by computing four laminar-flow cases; supersonic flow over a flat plate, supersonic flow in a diffuser, hypersonic flow over a 15-deg ramp, and hypersonic flow in a converging inlet. Extensive comparisons of heat transfer, skin friction, and pressure coefficients are made between Osher's and Roe's upwind schemes. For this class of flows, Osher and Roe upwinding yield very similar results.