New multigrid smoothers for the Oseen problem

We investigate the performance of smoothers based on the Hermitian/skew-Hermitian (HSS) and augmented Lagrangian (AL) splittings applied to the Marker-and-Cell (MAC) discretization of the Oseen problem. Both steady and unsteady flows are considered. Local Fourier analysis and numerical experiments on a two-dimensional lid-driven cavity problem indicate that the proposed smoothers result in h-independent convergence and are fairly robust with respect to the Reynolds number. A direct comparison shows that the new smoothers compare favorably to coupled smoothers of Braess-Sarazin type, especially in terms of scaling for increasing Reynolds number.