High order approximations of the vortical flow field and resulting aerodynamic coefficients of complex supersonic vortical flows, are computed using the Implicit Parabolized Navier-Stokes solver (IMPNS). Third and fifth order Weighted Essentially Non-oscillating (WENO) schemes for evenly spaced and for stretched structured meshes are employed for the approximate Riemann solution of the inviscid cross flow fluxes. An approximate Riemann solution is obtained using the Osher and Solomon solver and the one-equation Spalart-Allmaras turbulence model is modified for an improved strain-vorticity approximation. Results indicate that even on much coarser meshes the 5$^\text{th}$ order PNS-WENO-Spalart-Allmaras approach may achieve results that are superior to previously published full Navier-Stokes solutions that employ a two-equation RANS model but the additional computational demand of schemes for non-uniform grids, may not be justifiable for smoothly varying 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 the resolution of the vortical structures.