AN ORTHOGONALITY-PRESERVING ADVANCING TREE-TYPE MESH GENERATION METHOD

Mesh generation, as a key technique for discretizing continuous geometric space, plays a vital role in the accuracy and efficiency of computational fluid dynamics simulations. With increasingly complex geometries under study, traditional mesh generation methods often suffer from issues such as element intersection and distortion in locally intricate regions. These solutions typically rely on manual adjustments or specialized algorithms, resulting in a low degree of automation. To address these limitations, this study proposes a potential field–based advancing layer technology. This method does not rely on background mesh support and eliminates the need for mesh partitioning even when dealing with complex geometries; only the surface mesh is required to achieve fully automatic two-dimensional mesh generation. First, a potential field model is established. Based on this model, tracing models for potential field lines and equipotential lines are constructed, with these lines serving as mesh edges to ensure orthogonality. The potential field information is then used to dynamically guide the advancing direction and step size of the front. Combined with the advancing layer technology, an anisotropic tree-type mesh is generated layer by layer. To validate the method, two-dimensional meshing was performed on a third-order Koch snowflake shape, as well as on both the symmetric plane and the wing trailing-edge plane of the same cruciform-wing missile. The results show that the method achieves fully automatic mesh generation for different geometries, with approximately 99% of the generated elements exhibiting good orthogonality. Compared to traditional partial differential equation–based mesh generation methods, the proposed approach demonstrates stronger adaptability to complex shapes and improves the mesh quality metric, the minimum angle, by about 10°. This research applies potential field theory to two-dimensional mesh generation for complex geometries, providing a theoretical foundation and a feasible pathway for the future development of fully automatic three-dimensional mesh generation technology based on potential fields.