Velocity-pressure coupling in finite difference formulations for the Navier-Stokes equations

A new numerical procedure for solving the two-dimensional, steady, incompressible, viscous flow equations on a staggered Cartesian grid is presented in this paper. The proposed methodology is finite difference based, but essentially takes advantage of the best features of two well-established numerical formulations, the finite difference and finite volume methods. Some weaknesses of the finite difference approach are removed by exploiting the strengths of the finite volume method. In particular, the issue of velocity-pressure coupling is dealt with in the proposed finite difference formulation by developing a pressure correction equation using the SIMPLE approach commonly used in finite volume formulations. However, since this is purely a finite difference formulation, numerical approximation of fluxes is not required. Results presented in this paper are based on first-and second-order upwind schemes for the convective terms. This new formulation is validated against experimental and other numerical data for well-known benchmark problems, namely developing laminar flow in a straight duct, flow over a backward-facing step, and lid-driven cavity flow. Copyright (C) 2010 John Wiley & Sons, Ltd.