UPWIND-BIASED FINITE-VOLUME TECHNIQUE SOLVING NAVIER-STOKES EQUATIONS ON IRREGULAR MESHES

New node-centered finite-volume discretizations of advective and diffusive derivatives on structured meshes with quadrilateral cells are presented. They are applied to the solution of Euler and full Navier-Stokes equations using a pseudotime-dependent approach. The advective derivatives are split and upwind biased. The most interesting aspect of the scheme lies in its ability to provide good accuracy on meshes with severe skewness and stretching distortions. A very sensitive detector is presented which is capable of selectively identifying shock waves and insufficiently resolved shear layers. It is used to automatically switch to a first-order upwind scheme in some regions and provides a sharp and monotone shock capture. Results obtained for plane and axisymmetric steady supersonic laminar flows are discussed. They include blunt-body flows, a shock/boundary-layer interaction, and a now over a compression earner.