Streamline tracing-based topology for anisotropic mesh generation

For computational fluid dynamics (CFD) numerical simulations of complex geometries, mesh generation faces numerous challenges, especially in generating high-quality anisotropic meshes in regions with complex boundaries. Selecting an appropriate topological structure is a key difficulty in the process of anisotropic mesh generation. Traditional methods for generating anisotropic mesh topologies mainly rely on heuristic ideas and prior knowledge, lacking theoretical support. This easily leads to problems such as poor mesh adaptability, intersection of mesh lines, and local distortion, which in turn limits the stability and quality of mesh generation. To address this bottleneck, based on the Poincaré conjecture and the Helmholtz theorem, this paper proposes a streamline-based topological structure, which is applied to mesh generation for complex geometries in CFD. This method introduces the characteristic of non-intersecting streamlines into the mesh generation process, effectively avoiding the problems of self-intersection of mesh lines and local distortion both theoretically and practically, and significantly improving the adaptive mesh generation ability. The experimental results show that when dealing with complex geometries, the proposed method not only significantly improves the mesh quality but also enhances the stability and reliability of the mesh generation process, demonstrating advantages that are incomparable to those of traditional methods.