An anisotropic mesh generation method based on streamline-tracking topology

Mesh generation is a critical step in the numerical simulation of computational fluid dynamics, with mesh quality directly affecting both computational efficiency and result accuracy. Traditional methods for mesh topology generation heavily rely on human expertise and heuristic algorithms, often lacking a rigorous mathematical foundation and theoretical underpinning. When confronted with complex boundaries, multi-scale features, and dynamic topological structures, these traditional methods frequently encounter issues such as poor mesh adaptability, intersecting mesh lines, localized distortions, degradation of mesh quality, and high costs associated with manual intervention. To address these challenges, this paper proposes an anisotropic mesh generation method based on streamline-tracking topology, aiming at achieving the automatic generation of high-quality three-dimensional mesh topologies. The core concept treats the mesh as a potential field, with the central task being the explicit formulation of this potential field. In this paper, the signed distance field, a scalar field, is obtained via Delaunay triangulation. By computing its gradient, an irrotational vector field (i.e., potential field) is constructed. Mesh topology is generated by tracking the gradient field along streamlines, which then guides the generation of anisotropic meshes. Notably, streamlines inherently do not intersect, effectively eliminating the common problem of mesh line crossings encountered in traditional mesh generation processes. Furthermore, experimental validation is conducted on several representative aerospace and biomedical geometries. The results demonstrate that the proposed method exhibits strong robustness, adaptability, and topological consistency, highlighting its promising potential for automatic, high-quality mesh generation of complex geometries.