On preconditioned iterative methods for unsteady incompressible Navier-Stokes equations

When the implicit finite difference scheme and linearization technique in conjunction with the artificial compressibility method are employed to discretize the unsteady incompressible Navier-Stokes equations, in each pseudo-time step, a structured system of linear equations is obtained and needs to be solved numerically. In this paper, preconditioning techniques are applied to solve such linear systems. Numerical example is given to illustrate the effectiveness of the proposed method. We also find that a combination of the linearization technique with the preconditioned GMRES method is quite efficient for the implicit finite difference discretization of the incompressible Navier-Stokes equations.