Automatic Multigrid Generation for an Unstructured Parallel Overset-Grid Solver

Abstract

We present an algorithm that automatically generates an algebraic multigrid for an unstructured parallel overset-grid solver. As the first step in the development of the algorithm, the special topological features of the matrix representing the overset grids are described and analyzed; during the mesh coarsening procedure, the geometrical information of the overlapping cells is employed in the generation of the automatic rules of agglomeration. As a result, the proposed algorithm has algebraical and geometrical elements. In contrast with most studies on algebraic multigrid methods, which typically ignore the geometrical information of the meshes, the technique proposed in this paper introduces a tool to explicitly investigate the effects of neglecting the mesh topology. In order to achieve massive parallel computation capabilities, we propose a domain-decomposed version of the original algorithm that features global indexing parallelism. Furthermore, in order to utilize unstructured meshes imported from general-purpose grid generators, an automatic cell-index renumbering algorithm is proposed, which allowed us to devise a more efficient agglomeration procedure. To illustrate the suitability and efficacy of the main proposed algorithm and associated methods, examples for two- and three-dimensional grids are presented and discussed. In specific, for comparison purposes and to demonstrate the necessity of considering the mesh topology in the generation of multigrids for overset-grid solvers, we present simulations of channel flows interacting with a cylinder.