SPECTRAL MULTIGRID TECHNIQUES FOR THE NAVIER-STOKES EQUATIONS

We present a spectral multigrid method for the effective solution of the Navier-Stokes equations for incompressible fluids. Here we consider the vorticity-streamfunction formulation. Discretization in time is performed by a second order semi-implicit scheme where the diffusive term is treated in an implicit manner while the convective term is evaluated explicitly. For the discretization of the resulting Stokes-type problem, we introduce a new spectral collocation method. This scheme is highly accurate and allows efficient solution by spectral multigrid methods. We propose an efficient finite difference preconditioner. Numerical results are presented which substantiate the usefulness of our concept.