A comparison between a pressure projection method and a fully coupled multigrid FEM Navier-Stokes solver

This paper provides an analysis of a projection method for the solution of the unsteady incompressible Navier-Stokes equations. We describe the incremental pressure projection method and we analyse the splitting errors due to the inexact boundary conditions on pressure and velocity fields. In order to improve the solution of the incremental pressure-projection method, we also introduce the rotational pressure-projection method and the penalty method. Moreover, we compare the solution of the projection methods with the one obtained with the Navier-Stokes coupled system. In particular, three specific flow patterns are considered. The first pattern is a simple model of a fluid subject to a gravity force. The second pattern is the motion of a fluid in a vertical duct, subject to gravity and to another force of the same magnitude, but in the horizontal plane. The third pattern is the motion of a fluid past a cylindrical obstacle. In the last case we analyse the numerical viscosity introduced with the method in order to verify that the instability driven by the convective term is still present.