Vortex Capturing Using PNS-WENO Schemes in Uniform and Non Uniform Mesh Formulations (Advances in Applied Mathematics and Mechanics, 2019)
High order approximations of the vortical flow field and resulting aerodynamic coefficientsof complex supersonic vortical flows, are computed using the Implicit Parabolized Navier-Stokessolver (IMPNS). Third and fifth order Weighted Essentially Non-oscillating (WENO) schemes forevenly spaced and for stretched structured meshes are employed for the approximate Riemannsolution of the inviscid cross flow fluxes. An approximate Riemann solution is obtained usingthe Osher and Solomon solver and the one-equation Spalart-Allmaras turbulence model is modifiedfor an improved strain-vorticity approximation. Results indicate that even on much coarser meshesthe 5$^\text{th}$ order PNS-WENO-Spalart-Allmaras approach may achieve results that are superiorto previously published full Navier-Stokes solutions that employ a two-equation RANS model but theadditional computational demand of schemes for non-uniform grids, may not be justifiable for smoothlyvarying meshes. The proposed PNS-WENO scheme combination provides a novel approach that is fast,accurate and robust, and that can substantially reduce numerical dissipation and improve theresolution of the vortical structures.