Research On Generation And Post-processing Techniques For Unstructured Meshes

Over the past decades, the finite element method, numerical methods for the solution of PDEs (Partial Differential Equations), such as the finite volume method, the finite difference method, the boundary element method, have become one of core research fields of scientific computing. As a pretreatment of applying these methods, mesh generation is still the major bottleneck in practice for its time-consuming ventures. It has been paid close attention to for nearly 50 years, and at present grown up to an independent research branch including multi-disciplinary knowledge.In this dissertation, according to the demand of HEDP (High End Digital Prototyping), a CAE system developed by the Center for Engineering and Scientific Computation, Zhejiang University, two key techniques on unstructured mesh generation are studied:(1) Unstructured hexahedral mesh generation techniquesAutomatic and high-quality hexahedral mesh generation for complex geometries is now a very difficult issue, and not better resolved even in commercial mesh generation software. In this dissertation, we revisit two common techniques for simple geometries. One is the sweep method, i.e. along a predefined path sweeping a quadrilateral surface mesh from the source to the target. The hexahedral mesh formed is structured in the sweeping direction. The other is the mapping method, i.e. to map a meshing problem of an irregular shape in physical space into the meshing problem of a regular shape in parametric space. The mesh structures in both spaces remain similar while their geometric coordinates are changed.(2) Mesh post-processing technologyMesh quality is the key factor to affect the efficiency, convergence and accuracy of numerical analysis. After applying a meshing algorithm, post-processing the resulting mesh to enhance its quality is commonly required before numerical analysis. Notes, here mesh post-processing specifically refers to mesh quality improvement. In this dissertation, geometric and topological improvement techniques are respectively studies for tetrahedral meshes. For geometric techniques, with mesh point coordinates taken as optimization variables, and local mesh quality merits taken as optimization functions, iterative optimization algorithms are performed to improve mesh quality by relocating mesh points. For topological techniques, there are adding points, deleting points, edge swap, face swap, and their combinations. The combination of Laplacian techniques, geometric techniques and topological techniques is applied to Delaunay meshes, and the effect of mesh quality improvement is demonstrated to be rather good.In addition, for the purpose of visual steering of mesh quality assessment, a mesh quality analyzer is designed and implemented. With the help of the analyzer, the users could find the defective or low-quality cells quickly, and analyze the mesh quality distribution more clearly.