High Re separated flow solutions using the Navier-Stokes and approximate equations

The present study is concerned with the numerical simulation of high Reynolds number weakly separated laminar flows. It is shown that a 'well designed' code can solve the complete Navier-Stokes (NS) equations and the 'more suitable' parabolized Navier-Stokes (PNS) equations with the same convergence rate, so that solving the full NS equations is recommended when dealing with a new problem. Furthermore, solutions to the classical boundary layer equations in vorticity-stream function form are obtained, which are regular through the separation point, i.e., do not encounter the Goldstein singularity at separation. Finally, for a very typical high Reynolds number weakly separated flow, it is shown that, in the presence of nonnegligible skewness in the body oriented computational grid, a PNS-type approximation still provides very reliable solutions, whereas an interacting boundary layer-type model provides results plagued by severe errors.