An Available Method on Numerical Solutions of the Viscous and Incompressible Flow with Large Reynolds Numbers--A Numerical Approach to Steady, two dimensional Vortex Flow Field

In this paper, an improved SOR method for solving Navier-Stokes equations of the steady, two dimensional flow with large Reynolds numbers is proposed. The method has the second order accuracy in the whole flow field and can avoid the divergence of the iterations. The vorticity and the streamfunction serve as the basic variables of the solution and theaccuracy of the convective terms is improved by using an available transformation of the central difference. As a numeal example, the flow in a square cavity is calculated for Reynolds numbers 200, 400, 1000 and 10000. A comparison of the obtaned results with those available in the literature is made. It is shown that the problems of flow with higher Reynolds number can be satisfactorily solved by the proposed ISOR method.