Unstructured Mesh Quality Improvement Algorithms

The quality of initial meshes generated by automatic mesh generation algorithms is usually not good enough for numerical simulations, thus affecting the accuracy and convergence of numerical simulations. Various mesh quality enhancement algorithms are proposed to connect the meshing process and the numerical simulation process, which take initial mesh as input, and output qualified meshes. Therefore, the study on mesh quality enhancement algorithms is of great significance. In this dissertation, three quality enhancement algorithms are proposed as follows for two most frequently used types of meshes, i.e. triangular surface mesh and tetrahedral volume mesh.(1) A pre-process is suggested to abstract the geometrical features of triangular surface meshes, thus to prohibit the movement of mesh points specified as features in mesh smoothing. The movement of a free mesh point is restricted in the tangent plane of a local manifold including the point. With this restriction, a mesh smoothing optimization model is built for the movement of the free points, and resolved by a deepest descent algorithm.(2) A tetrahedral mesh quality improvement algorithm is presented by combining the geometrical smoothing and the basic topologic transformations. Owing to a set of data structures for tetrahedral mesh, high efficiencies of the improvement algorithm is guaranteed. Moreover, some topology operations are adopted to eliminate different types of bad elements.(3) A new topology operation called small polyhedron reconnection (SPR) is introduced for tetrahedral mesh quality improvement in order to break the limitations of basic topology transformations. The schemes of small polyhedron formation and speedup of the SPR are detailed. Experiments show that satisfactory tetrahedral quality improvement performance is achieved with combination of the SPR, the geometrical smoothing and the basic topologic transformations,...