Algebraic multigrid methods for the solution of the Navier-Stokes equations in complicated geometries

The application of standard multigrid methods for the solution of the Navier-Stokes equations in complicated domains causes problems in two ways. First, coarsening is not possible to full extent since the geometry must be resolved by the coarsest grid used, and second, for semiimplicit time stepping schemes, robustness of the convergence rates is usually not obtained for the arising convection-diffusion problems, especially for higher Reynolds numbers. We show that both problems can be overcome by the use of algebraic multigrid (AMG) which we apply for the solution of the pressure and momentum equations in explicit and semiimplicit time-stepping schemes. We consider the convergence rates of AMG for several model problems and we demonstrate the robustness of the proposed scheme.