Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme

A new finite difference method for the discretization of the incompressible Navier-Stokes equations is presented. The scheme is constructed on a stagg ered-mesh grid system. The convection terms are discretized with a fifth-or der-accurate upwind compact difference approximation, the viscous terms are discretized with a sixth-order symmetrical compact difference approximatio n, the continuity equation and the pressure gradient in the momentum equati ons are discretized with a fourth-order difference approximation on a cell- centered mesh. Time advancement uses a three-stage Runge-Kutta method. The Poisson equation for computing the pressure is solved with preconditioning. Accuracy analysis shows that the new method has high resolving efficiency. Validation of the method by computation of Taylor's vortex array is presen ted. Copyright (C) 1999 John Wiley & Sons, Ltd.