Stabilized velocity-correction methods for incompressible flows based on a discrete pressure Poisson equation

At the continuous level, from the Navier-Stokes equations for incompressible flows (the momentum and continuity equations) a pressure Poisson equation (PPE, from now onwards) can be obtained. An alternative system to the classical Navier-Stokes equations can be the momentum equation together with the PPE instead of the continuity equation....