Multigrid acceleration of an upwind Euler solver on unstructured meshes

Abstract

Multigrid acceleration has been implemented for an upwind flow solver on unstructured meshes. The flow solver is a straightforward implementation of Barth and Jespersen's unstructured scheme, with least-squares linear reconstruction and a directional implementation of Venkatakrishnan's limiter. The multigrid scheme itself is designed to work on mesh systems that are not nested, allowing great flexibility in generating coarse meshes and in adapting fine meshes. A new scheme for automatically generating coarse unstructured meshes from fine ones is presented. A subset of the fine mesh vertices is selected for retention in the coarse mesh. The coarse mesh is generated incrementally from the fine mesh by removing one rejected vertex at a time. In this way, a valid coarse mesh triangulation is guaranteed. Factors affecting multigrid convergence rate for inviscid flow are thoroughly examined, including the effect of the number of coarse meshes used, the type of multigrid cycle employed, the spatial discretization used on coarse meshes, and the nature of the flow. The present multigrid scheme is very successful in reducing computational time for inviscid flows in the subsonic and transonic regime. Nomenclature