Unstructured Mesh Generation and Manipulation Based On Elliptic Smoothing and Optimization
A Dissertation Presented for the Doctor of Philosophy in Computational Engineering, The University of Tennessee at Chattanooga
Mandar Sahasrabudhe, August 2008
The broad objective for this study was to develop techniques for generation and manipulation of quality unstructured meshes. Towards that goal, different mesh improvement algorithms were investigated.
Existing optimization based mesh smoothing strategies were investigated for improving overall mesh quality for unstructured meshes using different grid metrics, cost functions and point movement strategies. A new cost function and strategy for point movement was proposed for the mesh quality improvement problem, and the optimization strategy was also adapted and utilized for the purpose of generating quality viscous grids.
The main contribution of this study is to extend elliptic smoothing techniques, primarily used in structured grids, to unstructured grid technologies. Two new approaches were developed for performing elliptic smoothing on unstructured grids. The first approach used a global computational space which is created by utilizing a valid computational mesh. The second approach used a local computational space which involved using a virtual control volume at each node.
The elliptic smoothing scheme was extended with control functions and a Riemannian tensor field to manipulate general unstructured grids using a finite volume approach, and this approach was applied to the generation of quality viscous grids, generating a valid mesh from a tangled mesh, improving overall grid quality for inviscid grids, as a final step in the generation of inviscid grids, for grid movement of boundary movement/deformation problems and adaptation of unstructured grids using solution fields for problems in 2D/3D.