Numerical Solutions to the Incompressible Navier-Stokes Equations in Vorticity-Velocity form by Using the Group Explicit Iterative Method

Abstract

A numerical method for computing two-dimensional incompressible flows is presented. The steady vorticcity-velocity equations are discretized with the central finite difference approximation and the resulting equations are solved by using the Multi-Grid method with the Group-Explicit-Iterative method. The driven flow in a square cavity is used as a test problem. Calculations are carried out for the case with Reynolds number as high as 3200 on 257×257 grid points. The computed results are in good agreement with those based on the vorticity-stream function equations, and it is found that large residuals of the numerical solutions for the equation of continuity and the defining equation of vorticity occur near the corners on the moving surface.