Simulation in primitive variables of incompressible flow with pressure Neumann condition

A velocity–pressure algorithm, in primitive variables and finite differences, is developed for incompressible viscous flow with a Neumann pressure boundary condition. The pressure field is initialized by least-squares and updated from the Poisson equation in a direct weighted manner. Simulations with the cavity problem were made for several Reynolds numbers. The expected displacement of the central vortex was obtained, as well as the development of secondary and tertiary eddies