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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (1): 45-51.doi: 10.3969/j.issn.1005-3085.2016.01.005

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三维泡泡布点方法及网格生成 

沙鑫池,   聂玉峰,   张伟伟   

  1. 西北工业大学理学院应用数学系，西安 710129
  • 收稿日期:2014-06-12 接受日期:2015-01-22 出版日期:2016-02-15 发布日期:2016-04-15
  • 基金资助:
    国家自然科学基金 (11071196)；西北工业大学本科毕业设计重点扶持项目.

Node Placement Method by Bubble Simulation and Mesh Generation in Three-dimensional Region

SHA Xin-chi,  NIE Yu-feng,  ZHANG Wei-wei   

  1. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710129
  • Received:2014-06-12 Accepted:2015-01-22 Online:2016-02-15 Published:2016-04-15
  • Supported by:
    The National Natural Science Foundation of China (11071196); the Northwestern Polytechnical University Undergraduate Graduation Design Stress Support Project.

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摘要： 本文研究如何在三维区域上生成高质量的节点集并基于节点集进行网格生成．根据区域边界的几何描述和理想间隔控制函数，先后对曲面及区域内部用泡泡布点法进行节点布置．节点布置结束后，对区域边界的节点集运用高质量点集的局部网格生成算法(BLMG)进行网格剖分，对区域内部的点集直接进行Delaunay三角剖分．通过计算节点集生成Delaunay网格单元的质量来评价区域节点集的质量．泡泡均匀分布与非均匀分布的算例均表明，该算法生成的节点具有较高的质量并且在泡泡非均匀分布时具有很好的渐进性．

关键词: 泡泡布点方法, 网格剖分, 三维区域, 间隔函数

Abstract:

This paper studies how to generate high-quality node sets and use the nodes to generate the mesh in the three-dimensional region. According to the geometric description of the boundary region and the desired node-spacing function, the node placement method by bubble simulation is used on the surface and inside the area to layout the nodes successively. After the placement of the nodes distribution is finished, the bubble-type local mesh generate method and the Delaunay mesh method can be used to generate the mesh on the area surface and inside the area, respectively. Then quality of the bubble distribution is measured according to the quality of the Delaunay mesh. Numerical examples show that uniform node sets and non-uniform node sets generated by this method have high quality, and non-uniformly node sets obtained by this method have good gradualness.

Key words: node placement method by bubble simulation, mesh generation, three-dimensional region, node-spacing function

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