Robust coarsening of unstructured meshes for multigrid methods

Abstract

Multigrid techniques effectively accelerate steady-state convergence of unstructured mesh simulation of inviscid and viscous flows [6, 1, 4, 8, 31. In particuia, the aggiomeration multigrid method introduced by Venkatakrishnan and Mavriplis [8] is widely used with good success. Because agglomeration multigrid fuses fine mesh control volumes to form coarse mesh control volumes, & coarse unstructured mesh must be constructed. Unfortunately, the discretization of viscous terms on coarse agglomerated meshes requires an ad hoc modification compared with the 6ne mesh discretization. Whether this modification is precisely correct for the Reynolds-averaged Navier-Stokes equations is not clear, and application of agglomeration methods to problems outside fluid mechanics might require a different heuristic modification. produces a valid coarse mesh at each level, regardless of the fine mesh input and the number of coarse meshes generated. This new approach selects a subset of the fine mesh vertices for inclusion in the coarse mesh and removes excess vertices incrementally. The vertex sel&Ltion str&,tegy, desdribed in Se&ion 2, ret&in& important geometric and topologi&l features of the fine mesh. An especially useful feature is that anisotropic, pseudo structured sections of the mesh can be coarsened dir rectionally to improvecell aspect ratio. The incremental vertex deletion scheme, described in Section 3, also preserves fine mesh features in the coarse mesh. Each coarse mesh is post-processed using mesh reconnection and smoothing techniques to improve coarse mesh quality. Examples included in Section 4 demonstrate the capabilities of the new algorithm in both two and three dimensions.