Downwind Numbering : A Robust Multigrid Method for Convection-Diffusion Problems on Unstructured Grids

In the present paper we introduce and investigate a robust smoothing strategy for convection-diffusion problems in two and three space dimensions without any assumption on the grid structure. The main tool to obtain such a robust smoother is an ordering strategy for the grid points called “downwind numbering”, which follows the flow direction and -combined with a Gaus-Seidel type smoother - yields robust multi-grid convergence for adaptively refined grids, provided the convection field is cycle-free. The algorithms are of nearly optimal complexity and the corresponding smoothers are shown to be robust in numerical tests.