An efficient smoother for the Stokes problem Original Research Article

We present an efficient smoother for the solution of the Stokes problem by multigrid methods. The smoother is obtained from a variant of the pressure correction steps in SIMPLE type algorithms. On the other hand the complete SIMPLE iteration does not provide good smoothers. The differences give rise to a distinction of two types of iterations although the types are seldom encountered in their pure form. The differences are less significant in practical computations due to additional approximations. A smoothing and convergence rate O(m−1) is achieved where m denotes the number of smoothing steps. Here the usual pressure correction step in SIMPLE iterations is understood as a Jacobi type iteration. A Gauss-Seidel version has turned out to be more robust and preferable. This is obvious from our numerical results for stationary and instationary problems.