Implementation of the Divergence-Free and Pressure-Oscillation-Free Projection Method for Solving the Incompressible Navier-Stokes Equations on the Collocated Grids

Abstract

In this paper, a divergence-free and pressure-oscillation-free projection method for solving the incompressible Navier-Stokes equations on the non-staggered grid is presented. The exact discrete projection method is used to compute the velocity field, which ensures the discrete divergence of the velocity field is zero. In order to eliminate the odd-even decoupling in the pressure field, a filtering procedure is proposed and applied to the pressure field. We have shown this filter recovers the grid scale ellipticity in the pressure field and the odd-even decoupling can be removed effectively. The proposed numerical scheme is further verified through numerical experiments.