Multigrid Acceleration of an Upwind Euler Solver on Unstructured Meshes

Multigrid acceleration has been implemented for an upwind ow solver on unstructured meshes. The ow solver is a straightforward implementation of Barth and Jespersen's unstructured scheme, with least-squares linear reconstruction and a directional implementation of Venkatakr-ishnan's limiter. The multigrid scheme itself is designed to work on mesh systems which are not nested, allowing great exibility in generating coarse meshes and in adapting ne meshes. A new scheme for automatically generating coarse unstructured meshes from ne ones is presented. A subset of the ne mesh vertices are selected for retention in the coarse mesh. The coarse mesh is generated incrementally from the ne mesh by removing one rejected vertex at a time. In this way, a valid coarse mesh triangula-tion is guaranteed. Factors aaecting multigrid convergence rate for inviscid ow are thoroughly examined, including the eeect 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 ow. The present multigrid scheme is very successful in reducing computational time for inviscid ows in the subsonic and transonic regime.