Block preconditioners for the discrete incompressible Navier–Stokes equations

We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier–Stokes equations. For steady-state problems, we show that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. These characteristics are directly correlated with the convergence properties of iterative solvers, with convergence rates independent of mesh size and only mildly dependent on viscosity. For evolutionary problems, we show that implicit treatment of the time derivatives leads to systems for which convergence is essentially independent of viscosity. Copyright © 2002 John Wiley & Sons, Ltd.