Smoothers in Coupled Multigrid Methods for the Stokes and Navier-Stokes Equations

Volker John
Lutz Tobiska
Otto-von-Guericke-Universität Magdeburg, Germany


Coupled multigrid methods have been proven as efficient solvers for the incompressible Navier-Stokes equations in recent benchmark computations. This paper presents a numerical study of two classes of smoothers in these methods. The class of Vanka-type smoothers is characterized by the solution of small local linear systems of equations in a Gauss-Seidel manner in each smoothing step whereas the Brass-Sarazin-type smoothers solve a large global saddle point problem. The behaviour of these smoothers with respect to computing times and parallel overhead is studied on 2d DFG benchmark problems of flows around a cylinder.

Keywords. Incompressible Navier-Stokes equations, parallel coupled multigrid methods, Vanka-type smoothers, Braess-Sarazin-type smoothers.

Contributed November 5, 1998.