A comparison of single and multi-sweep techniques for reduced Navier-Stokes equations

The reduced Navier-Stokes equations obtained by dropping stream-wise diffusion terms are shown to still possess an elliptic nature resulting from a pressure interaction. If these equations are solved using a single-sweep algorithm a severe stability problem is encountered due to the equations not being well posed. The governing equations may be further reduced to remove the elliptic pressure interaction, enabling a very efficient single-sweep scheme to be used without such a stability problem. A multi-sweep method is developed which allows the full pressure interaction to be retained, without the stability problems.