基于八叉树细化的高效四面体网格生成

刘金宝; 高翔; 张翔; 龚春叶

doi:10.7638/kqdlxxb-2024.0020

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基于八叉树细化的高效四面体网格生成

研究论文 | 更新时间：2026-05-28

- 基于八叉树细化的高效四面体网格生成
- Efficient tetrahedral mesh generation algorithm based on octree refinement
- 空气动力学学报 2025年43卷第8期页码：50-58
- 作者机构：
  
  1. 国防科技大学计算机学院,长沙,410073
  2. 国防科技大学高端装备数字化软件湖南省重点实验室,长沙,410073
- 作者简介：
  
  刘金宝（1992—），男，山东郯城人，工程师，研究方向：网格生成理论与算法. E-mail：807660872@qq.com
  高翔*，助理研究员，研究方向：大规模科学工程计算与网格生成. E-mail：gaoxiang12@nudt.edu.cn
- 基金信息：
  
  国家重点研发计划（2023YFB3001903）;国家自然科学基金（12102467）
- DOI：10.7638/kqdlxxb-2024.0020
  中图分类号： O241;V211.3
- 纸质出版：2025
- 稿件说明：
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刘金宝, 高翔, 张翔, 等. 基于八叉树细化的高效四面体网格生成[J]. 空气动力学学报, 2025, 43(8): 50−58.

LIU Jinbao, GAO Xiang, ZHANG Xiang, et al. Efficient tetrahedral mesh generation algorithm based on octree refinement[J]. 2025, 43(8): 50-58.
刘金宝, 高翔, 张翔, 等. 基于八叉树细化的高效四面体网格生成[J]. 空气动力学学报, 2025, 43(8): 50−58. DOI： 10.7638/kqdlxxb-2024.0020

LIU Jinbao, GAO Xiang, ZHANG Xiang, et al. Efficient tetrahedral mesh generation algorithm based on octree refinement[J]. 2025, 43(8): 50-58. DOI： 10.7638/kqdlxxb-2024.0020.

摘要

非结构化四面体网格在复杂几何建模中具有重要应用价值，但现有方法多数需要先生成表面网格，再基于表面网格生成体网格，在大型复杂模型的高精度仿真中往往会出现三维网格生成出错或规模过大的情况。为了克服现有技术中网格生成效率低、鲁棒性较差、实现过程复杂等缺陷，本文提出了一种基于八叉树细化的非结构化四面体网格生成算法。算法采用改进的根四面体网格形状，在保证网格质量的同时使得初始网格单元形状一致，在表面拟合阶段采用网格形状调整和网格分裂两个步骤的实现方式。测试结果表明，本算法可以忽略部分几何模型缺陷，0.9～1.0高质量区间的网格单元占比明显高于其他方法，百万级网格生成耗时较传统方法减少80%以上。该算法能够高效地生成高质量网格，并克服了传统方法的局限性，为非结构化四面体网格生成领域的研究和应用提供了新的思路和参考。

Abstract

Unstructured tetrahedral meshes hold significant application value in complex geometric modeling

yet most existing methods require prior surface mesh generation before volume mesh construction

often leading to 3D mesh generation failures or excessive scale in high-precision simulations of large complex models. To overcome limitations in current techniques

such as low efficiency

poor robustness

and implementation complexity

this paper proposes an octree-refinement-based unstructured tetrahedral mesh generation algorithm. The algorithm adopted an improved root tetrahedral configuration ensuring shape consistency among initial grid units while maintaining quality. Surface fitting was achieved through two operational phases: mesh shape adjustment and mesh splitting. Test results demonstrated the algorithm's tolerance to certain geometric defects

exhibiting a significantly higher proportion of high-quality elements (0.9–1.0 metric range) than other methods

while reducing mesh generation time by over 80% for million-element meshes compared to conventional methods. This approach provides an efficient high-quality mesh generation solution that overcomes traditional limitations

offering new perspectives for research and applications in unstructured tetrahedral mesh generation.

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references

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