Fourth-order compact formulation of Navier-Stokes equations and driven cavity flow at high Reynolds numbers

A new fourth-order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes equations can easily be applied to this fourth-order compact formulation. In particular, in this work the formulation is solved with an efficient numerical method that requires the Solution of tridiagonal systems using a fine grid mesh of 601 x 601. Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number with Re = 20000 fourth-order spatial accuracy. Detailed solutions are presented. Copyright (c) 2005 John Wiley & Sons, Ltd.