High Reynolds number separated flow solutions using Navier-Stokes and approximate equations

The present study is concerned with the numerical simulation of high Reynolds number, two-dimensional, incompressible, steady, weakly separated laminar flows. It is shown that a “well-designed” code can solve the complete Navier-Stokes equations and the parabolized vorticity equations with the same convergence rate, so that solving the full Navier-Stokes equations is recommended when dealing with a new problem. Furthermore, the boundary-layer equations in vorticity/stream-function form are solved without encountering the Goldstein singularity at separation. Finally, for a typical high Reynolds number weakly separated flow, it is shown that, in the presence of a non-negligible skewness in the body-oriented computational grid, the parabolized vorticity approximation still provides very reliable solutions, whereas an interacting boundary-layer model provides results plagued with severe errors.