Algebraic multigrid, mixed-order interpolation, and incompressible fluid flow

This paper presents the results of numerical experiments on the use of equal-order and mixed-order interpolations in algebraic multigrid (AMG) solvers for the fully coupled equations of incompressible fluid flow. Several standard test problems are addressed for Reynolds numbers spanning the laminar range. The range of unstructured meshes spans over two orders of problem size (over one order of mesh bandwidth). Deficiencies in performance are identified for AMG based on equal-order interpolations (both zero-order and first-order). They take the form of poor, fragile, mesh-dependent convergence rates. The evidence suggests that a degraded representation of the inter-field coupling in the coarse-grid approximation is the cause. Mixed-order interpolation (first-order for the vectors, zero-order for the scalars) is shown to address these deficiencies. Convergence is then robust, independent of the number of coarse grids and (almost) of the mesh bandwidth. The AMG algorithms used are reviewed. Copyright (C) 2009 John Wiley & Sons, Ltd.