Unstructured Surface Mesh Generation Based On Geometric Decompostion

Numerical simulation plays an increasingly important role in various scientific computing and engineering designs,and mesh generation is the pre-processing of numerical simulation and the main performance bottleneck in the application of the latter.In the development of mesh generation technology,unstructured meshes are widely used in numerical simulation practice in different fields because of their strong ability to adapt to complex geometry and good automaticity of generation algorithm.The surface mesh is mainly applied to model the surface problems of geometric models,and is also the input condition for modeling 3D solid problems.The quality of surface mesh cells is crucial to the whole numerical simulation,and has been the main content of mesh generation research.In engineering applications,especially in fields such as computational fluid dynamics and computational electromagnetics,computational meshes containing tens or even hundreds of millions of degrees of freedom need to be generated for more detailed simulations and analyses,which places great demands on the efficiency and robustness of mesh generation.To this end,this paper proposes a method for generating unstructured surface meshes based on geometric decomposition,and discusses several issues such as the quality of mesh cell generation and the feasibility and robustness of the algorithm.The main contributions are as follows:(1)The generation of 2D planar triangular mesh cells is systematically studied.Based on the idea of geometric decomposition,this paper proposes an algorithm for generating two-dimensional planar triangular mesh cells and implements an automated procedure for mesh generation corresponding to it.The important implementation details of the algorithm and the complexity of the algorithm are discussed based on the implementation steps and test case demonstrations of the algorithm.(2)For the 3D surface mesh generation,this paper is based on the idea of mapping method,which maps each surface of the geometric model to the 2D plane one by one,and then uses the proposed 2D plane triangle mesh generation algorithm to get the triangle cell mesh of the parameter plane,and then mapping back to the 3D surface.For the 3D surface mesh obtained by the mapping method,the study implements a mesh quality optimization method,which makes the final generated mesh cells have high quality.(3)For the algorithm and implementation procedure proposed in this paper,a series of typical cases of 3D surface geometry models in numerical simulations like computational fluid dynamics and structural mechanics are used,and based on the widely used mesh quality evaluation method,a test analysis is conducted and compared with the common algorithm in the open-source mesh generation software Gmsh to verify the feasibility and robustness of the algorithm in engineering practice and scientific computation.