Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation

摘要

A method of unstructured tetrahedral mesh generation for general three-dimensional domains is presented. A conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology. The geometry of the surfaces is represented either analyticaIly or by piecewise polynomial interpolation. A preliminary surface mesh is generated by an advancing-front method, with the nodes inserted by hard-sphere packing in physical space in accordance with a prescribed mesh density. Interior nodes are inserted in a face-centered-cubic (FCC) crystal lattice arrangement coupled to octree spatial subdivision, with the local lattice parameter determined by a prespecified nodal density function. Prior to triangulation of the volume, the pre- liminary surface mesh is preprocessed by a combination of local transformations and subdivision in order to guarantee that the surface triangulation be a subcomplex of the volume Delaunay triangulation. A joint Delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing-front approach. The resulting mesh is finally improved upon by the application of local transformations. The overall time complexity of the mesher is O(N log N). The robustness and versatility of the approach, as well as the good quality of the resulting meshes, is demonstrated with the aid of selected exam- ples.