Finite difference scheme for the solution of fluid flow problems on non‐staggered grids

Abstract

A new finite difference methodology is developed for the solution of computational fluid dynamics problems that do not require the use of staggered grid systems. Previous successful and robust non-staggered methods, which used primitive variables and mass conservation in order to solve the pressure field, either interpolate cell-face velocities or interpolate the pressure gradients in a special way, usually with an upwind-bias to avoid the problem of odd–even coupling between the velocity and pressure fields. The new methodology presented does not detail a ‘special interpolation procedure for a primitive variable’, however, it manages to avoid the problem of odd–even coupling. The odd–even coupling is avoided by applying fourth-order dissipation to the pressure field. It is shown that this approach can be regarded as a modified Rhie and Chow scheme. The method is implemented using a SIMPLE-type algorithm and is applied to two test problems: laminar flow over a backward-facing step and laminar flow in a square cavity with a driven lid. Good agreement is obtained between the numerical solutions and the corresponding benchmark solutions. The pressure dissipation term was found to successfully suppress wiggles in the pressure field. Copyright © 2000 John Wiley & Sons, Ltd.