Adaptive Tetrahedral Mesh Generation Algorithm Base On Geometric Features

For geosciences mechanism and process model simulation and analysis, most of them are done by meshing the geographic spatial objects, applying FEM and other numerical methods to obtain the numerical solution. Differed from geometric objects in mechanical engineering applications, geosciences objects are generally having complex boundaries and space feature constraints. The traditional two-dimensional GIS using a two-dimensional spatial data model is difficult to describe and express the real three-dimensional phenomena, and the existing three-dimensional geological model construction and mesh generation method, which serve for the mesh geometric expression or mesh generation, are considering more about the geometric characteristics of geosciences objects, will not combine voxel-based data model with the mathematical model supporting scientific computing.In order to simulate complex phenomena express and analyze its change characteristics more realistically, to promote the development of three-dimensional GIS geosciences analysis and support the geosciences calculation based on the finite element method and other numerical methods efficiently, this paper propose the research on tetrahedral mesh generation and its self-adaptation algorithm, for the requirement on mesh quality of geosciences objects characteristics as well as the finite element method and other numerical calculation, based on the research on the of curved surface adaptive mesh generation method for the surface of the STL model, studying the Delaunay adaptive tetrahedral mesh generation method considering feature constraints. The results achieved include the following:(1) Take STL model as an example for discrete curved surface model, get its Riemannian metric through the identification and reconstruction of sub-domain surface, extract the geometric features and build the geometric adaptive size field, adaptively discrete sub-domain boundaries, generate parameter plane using Delaunay method based on the Riemannian metric, achieve curved surfaces adaptive mesh generation method for the STL model, eliminating the mapping distortion and generating the adaptive surface mesh with appropriate size and rational density transition.(2) By comparing the2D Delaunay triangulation mesh having lost the constrained faces with the triangle surface in the tetrahedral mesh, apply the Delaunay method to find the missing sub constrained surface, insert nodes in the constrained edge and the constrained surface to achieve the recovery of the lost boundary constraints and internal feature constraints, achieving tetrahedral mesh generation method considering feature constraints, having reduced the difficulty of constraints recovery and given the tetrahedral quality optimization method to improve the quality of the mesh.(3) Based on adaptive surface mesh based, build the grid size field by considering model surface geometric size and the size control specified by internal feature constraint, on this basis, continue to choose the best tetrahedron triangle surface, adaptively generate appropriate internal node in one of its sides, apply the BW method to insert internal nodes, and then achieving the adaptive tetrahedral mesh generation method.It’s proved by instance analysis that this study on tetrahedral mesh generation and adaptive algorithm is reliable and efficient, to some extent meeting the requirement for three-dimensional grid mesh of GIS and geosciences analysis calculation and simulation.