Flux-Limited Schemes for the Compressible Navier-Stokes Equations

Several high-resolution schemes are formulated with the goal of improving the accuracy of solutions to the full compressible Navier-Stokes equations. Calculations of laminar boundary layers at subsonic, transonic, and supersonic speeds are carried out to validate the proposed schemes. It is concluded that these schemes, which were originally tailored for nonoscillatory shock capturing, yield accurate solutions for viscous flows. The results of this study suggest that the formulation of the limiting process is more important than the choice of a particular flux splitting technique in determining the accuracy of computed viscous flows. Symmetric limited positive and upstream limited positive schemes hold the promise of improving the accuracy of the results, especially on coarser grids.