A review of marching procedures for parabolized Navier-Stokes equations

Marching techniques for the parabolized Navier Stokes equations are considered. With the full pressure interaction and prescribed edge pressure these equations are weakly elliptic in subsonic zones. A minimum marching step size (delta x sub min), proportional to the total thickness of the subsonic layer, exists. However, for thin subsonic boundary layers (Y sub M = 1) and with delta x = 0(Y sub M), stable and accurate solutions are possible. With forward differencing of the axial pressure gradient the procedure can be made unconditionally stable; a global iteration procedure, requiring only the storage of the pressure term, has been demonstrated for a separated flow problem. Solutions for incompressible boundary layer-like flows, for internal flows, and for supersonic flow over a cone at incidence with a coupled strongly implicit procedure are presented.