Numerical performance of smoothers in coupled multigrid methods for the parallel solution of the incompressible Navier-Stokes equations

In recent benchmark computations [Schafer M, Turek S. The benchmark problem 'Flow around a cylinder'. In flow Simulation with High-Performance Compute rs II, Hirschel EH (ed.), vol. 52 of Notes on Numerical Fluid Mechanics. Vi eweg: Wiesbaden, 1996; 547-566], coupled multigrid methods have been proven as efficient solvers for the incompressible Navier-Stokes equations. A num erical study of two classes of smoothers in the framework of coupled multig rid methods is presented. The class of Vanka-type smoothers is characterize d by the solution of small local linear systems of equations in a Gauss-Sei del manner in each smoothing step, whereas the Brass-Sarazin-type smoothers solve a large global saddle point problem. The behaviour of these smoother s with respect to computing times and parallel overheads is studied for two -dimensional steady state and time-dependent Navier-Stokes equations. Copyr ight (C) 2000 John Wiley & Sons, Ltd.