一种保正交性的生长型叉树网格生成方法
AN ORTHOGONALITY-PRESERVING ADVANCING TREE-TYPE MESH GENERATION METHOD
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摘要: 网格生成作为将连续几何空间离散化的关键技术, 对计算流体力学数值模拟的精度与效率至关重要. 随着研究对象外形日趋复杂, 传统网格生成方法在局部几何复杂区域常出现单元相交、畸变等问题, 其解决方法往往依赖人工调整或特殊算法, 自动化程度较低. 为此, 研究提出一种基于有势场的前沿层进法. 该方法无需背景网格辅助, 在面对复杂外形时亦无需进行网格分区, 仅需给定网格边界即可实现全自动二维网格生成. 首先建立了有势场模型, 并基于该模型构建了有势场线与等势线追踪模型, 将场线与等势线作为网格线以确保网格的正交性; 进而以有势场信息动态指导阵面推进方向与步长, 结合前沿层进法逐层生成生长型各向异性叉树网格. 为验证方法有效性, 分别对三阶科赫雪花外形、十字翼形导弹对称面外形及翼型尾截面外形进行了二维网格剖分. 结果表明: 在面对不同外形时, 可完成全自动网格剖分, 且生成网格中约99%的单元具有良好正交性; 相较于传统偏微分方程网格生成方法, 所提方法对复杂外形的适应性更强, 能将网格质量指标最小内角提升约10°. 该研究将势场理论应用于复杂外形二维网格生成, 为后续发展基于有势场的三维全自动网格生成技术提供了理论基础与可行路径.Abstract: 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.
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