A direct one-step pressure actualization for incompressible flow with pressure Neumann condition

We develop a velocity-pressure algorithm, in primitive variables and finite differences, for incompressible viscous flow with a Neumann pressure boundary condition. The pressure field is initialized by least-squares and up-dated from the Poisson equation in one step without iteration. Simulations with the square cavity problem are made for several Reynolds numbers. We obtain the expected displacement of the central vortex and the appearance of secondary and tertiary eddies. Different geometry ratios and a 3D cavity simulation are also considered.