A density-controlled triangular and quadrilateral element mesh automatic generation system

We made an intensive study to develop an automatic mesh generation system based on the theory of Voronoi diagram and front advancing. The objective of this system is to create meshes for numerical modeling of practical engineering problems in the fields of geomechanics, hydrology, hydraulics, and water resources. The input data of the system is a set of given points to form the boundary contour of the analyzed geometry, containing the coordinates, the connections and the point spacing specified by users. Boundary points are generated by recursively inserting midpoints according to the spacing of the input points. For the curved boundaries, B-splines are constructed to interpolate midpoints. For the geometries with concave features and long thin domains, boundary loss problem may occur after generating the Voronoi diagram of boundary points. This problem is resolved by recursively inserting pseudo-points at the midpoints of the missing edges until all the original boundary edges are fully described. In order to ensure the curvature accuracy of curved boundaries, pseudo-points should be eliminated again by corresponding modes. Two criteria for selecting removal modes are employed, the Jacobian and minimum angle. Two methods are used to generate interior points. One is direct method and the other is pre-test method. A comparison of the two methods is also made. Laplacian method is used to smooth the interior points of triangles. For the geometries with several sub-domains, it is required to ensure the conformity of the elements and points on the intersecting boundaries between adjacent sub-domains. We establish corresponding methods to treat the overlapped boundary edges and implement the reasonable distribution and excellent conformity of the triangles and points on the overlapped boundaries. On the basis of the triangular mesh created by Delaunay triangulation, a front-advancing method is used to further generate quadrilateral mesh by combining two connected triangles. To ensure the quality of quadrilateral mesh, certain rules are established to determine the triangle pairs for combination layer by layer. After the initial combination, there are always triangles that have not been combined. To treat the remaining triangles, corresponding moving method is established to move each remaining triangle to its closest one by destructing and reconstructing contiguous quadrilaterals and combine them until there is no more than one triangle remained. The optimization modes are employed to improve the topological connections of the boundary quadrilaterals with three points on the same edge. Finally, Laplacian method is used to smooth the interior points of the quadrilateral mesh. The accuracy and reliability of the developed system are demonstrated with many meshing examples for the geometries with sub-domains and curved boundaries normally encountered in subsurface media.