Abstract: Using the preconditioning technique,the unsteady incompressible Navier-Stokes equations are solved by a dual time stepping method.An implicit line Gauss Seidel relaxation method is designed to advance the equations in pseudotime steps.The convective flux is computed by a flux difference splitting based third order upwind scheme.Based on the numerical simulation for the Lid driven cavity flow at different Reynolds numbers,the convergence characteristics of the preconditioning algorithm for solving incompressible viscous flows is studied numerically.

Key words: unsteady incompressible Navier Stokes equations, preconditioning, numerical simulation