FINITE-DIFFERENCE SOLUTIONS OF THE NAVIER-STOKES EQUATIONS ON STAGGERED AND NON-STAGGERED GRIDS

Finite difference schemes for the Navier-Stokes equations are considered, with particular attention to the discretization of the pressure gradient and divergence terms. It is demonstrated that the relation between these terms is the principal reason for the use of the conventional staggered mesh with SIMPLE and other schemes. The important factors in the differencing are that it should lead to an elliptic scheme that satisfies the integrability constraint. The SIMPLE scheme automatically satisfies these two constraints. A non-staggered mesh scheme that also satisfies these constraints has been developed. Comparisons between it and a SIMPLE scheme for natural convection in a cavity indicate that the schemes have equivalent accuracy. For the non-uniform mesh used in this problem the non-staggered scheme is more efficient. It is expected that this increase in efficiency would be greater for adaptive and multi-grid algorithms.