| This report describes the development, implementation, and evaluation of a multigrid method for three dimensional, time dependent, incompressible fluid flow on unstructured meshes. The benefits of multigrid methods have been known to numerical analysts for several years. Multigrid has been applied to problems in the field of Computational Fluid Dynamics almost since its inception. In both the structured and unstructured grid communities, multigrid has enjoyed widespread popularity and success. The unstructured applications, however, all have been static in the sense that they do not involve moving bodies and transient remeshing.; The use of multigrid in fully transient flow problems requires a procedure for the dynamic generation of coarse meshes. In the world of structured grids, where coarse meshes can be generated rapidly with minimal effort, this requirement can be met quite easily. In contrast, such a procedure has been the major obstacle in the realization of a fully time dependent multigrid solver for unstructured meshes. Previous research has led to a small number of unstructured grid coarsening schemes. However, these schemes, while powerful, are too expensive and/or cumbersome to be used in anything but static flow problems. Furthermore, they can require additional preprocessing time on the part of the user.; As part of this work, a robust, efficient, and fully automated coarsening algorithm for tetrahedral meshes has been developed. This algorithm has enabled the application of multigrid methods to fully transient flow problems with remeshing. An additional capability is that the additional user preprocessing necessary with more traditional coarsening strategies is completely eliminated. Multigrid can be enabled as a simple run-time option with no additional user input. As is demonstrated, the resultant flow solver allows multigrid methods to be used to solve complex flow problems of practical engineering importance in a manner completely transparent to the user. |
