用于边界面法的三维体网格生成方法
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摘要
基于边界积分方程的边界面法具有很多优点。一般边界面法只需要离散问题域的表面,并且可以采用不连续单元。因此,用于边界面法的网格生成方法可以更加灵活。边界面法在分析非线性问题和非均质问题时,需要三维网格来进行体积分,并且需要三维网格进行后处理显示。在三维网格生成的研究中,目前已可以实现复杂实体的四面体网格自动生成。六面体单元能够获得更好的计算结果,但全六面体网格的自动生成依然是一个难点。要得到复杂实体的全六面体网格,需要通过大量的人机交互才能完成。因此,本文在用于边界面法的三维网格自动生成方面做了一系列的尝试和探索。同时,利用边界面法的优点,尝试采用一些特殊的单元,达到降低网格生成难度,提高效率的目的。本文主要完成了以下研究工作：
(1)为实现对复杂三维实体的网格自动生成,本文构建了一个三维网格生成框架。该框架分为网格数据管理、特征识别、虚拟分解和网格生成方法四个部分。本文设计了一个统一的数据管理器来管理网格数据,很好地实现了数据存储量和数据获取所需的计算量之间的平衡。统一的网格数据管理让程序的调整、维护和扩充十分便捷。在该框架中可以实现各种三维网格生成方法,可以将所得的网格单元转换为计算单元,并且可以导出到其他模块。
(2)为实现对复杂三维实体的四面体网格自动生成,本文提出了一种采用推进波前法生成域内点的Delaunay方法。该方法采用推进波前法来生成域内点,采用Delaunay内核将该点插入到网格中。本文加入了对前沿的识别,筛选出适合用来生成新点的前沿,剔除不满足要求的前沿,提高了算法的效率。该方法能够生成高质量的网格,具有较高的效率并且可以保证网格生成的收敛。
(3)为完成对复杂三维实体的六面体网格自动生成,本文提出了网格特征的概念,并构造了网格特征的识别方法。该方法能够从复杂三维实体中识别出可扫掠部分,并且可以自动识别出扫掠体的源面、目标面和连接面。然后采用虚拟体分解技术将可扫掠部分从实体中分解出来。分解得到的可扫掠子域可以采用扫掠法生成六面体网格。对分解得到子域全部可扫掠的情况,就可以实现六面体网格的自动生成。
(4)为实现了对含有细小管道的三维实体的网格自动生成,本文提出了一种混合网格自动生成方法。同时构造了一种五面体网格的生成方法来解决四面体网格和六面体网格之间的相容性问题。该方法在管道周围生成六面体网格,用四面体单元对剩余区域进行填充,采用金字塔五面体单元来连接这两种网格。该方法能够完成对含有细小管道的三维实体的高质量网格自动生成。为采用边界面法对含有细小管道的三维实体进行弹性力学分析,本文构造了管单元和含有空缺的三角形单元。采用这两种计算单元,降低了计算网格的生成难度,在提高了计算效率的同时有很高的计算精度。
(5)为了能够完成对混凝土坝的自动分析,采用本文的方法,通过特征识别,自动完成了对子域网格生成方法的判断,从而实现了对整个混凝土坝的三维网格自动生成。基于生成的网格,采用边界面法完成了对混凝土坝浇筑建造过程的模拟。
The boundary face method (BFM) based on the boundary integral equation (BIE) exhibits some extraordinary merits. Generally, the BFM only needs to discretize the boundary of the domain. And the mesh can be obtained by discretizing each piece wise continuous panel of the body's surface without restriction of element connectivity, hence, considerably simplifies the discretization task and the mesh generation method can be much more flexible. BFM also needs three-dimensional mesh to carry out the postprocess and analysis. The tetrahedral mesh can be generated automatically for complex solids. All-hexahedral meshes are preferred than tetrahedral mesh. But all-hexahedra meshing methods have proven to be more challenging. In order to discretize a complex solid, the volume needs to be decomposed manually, which is a time consuming and difficult task. Therefore, this dissertation conducts some useful researches and trials on the automatical three-dimensional mesh generation method for BFM. Based on the advantages of the BFM, some special elements are used to discretize the boudray of the domain. Hence, the discretization of the surface is very simple, resulting in substantial savings in both data preparation and computing costs. As a result, the following studies are carried out in this dissertation.
(1) In order to construct an automatical mesh generator, a program framework for three-dimensional mesh generation is developed. In the framework, some C++classes are designed to performing different tasks needed in overall mesh generation, such as mesh data management, feature recognition, virtual decomposition, and mesh generation methods. A mesh data manager is developed, the conflicting requirements of compactness and computational efficiency is well balanced. The uniform mesh database is convenient for modification, maintenance and expansion of the programme. A variety of three-dimensional mesh generation methods can be implemented in this framework. The resulting mesh cells can be converted into elements for analysis and dumped to postprocess module.
(2) A Delaunay method coupled with the advancing front method for automatical tetrahedral mesh generation is presented. The internal points are created by advancing front method and inserted into the mesh by Delaunay kernel procedure. To get better efficiency, a front identification and field point generation method is proposed and applied. The background mesh is used to specify mesh size distributions over arbitrarily shaped domains. The grid is applied to manage the background mesh, thus the point can be quickly located in the backgroud mesh. The mesh generation method combines the advantages of the high point placement quality of the advancing front method and the high efficiency and convergence guaranty of the Delaunay algorithm.
(3) The sweep method is applied to generate hexahedral mesh. The mesh feature recognition method is proposed to recognize the sweepable part from the complex solid. And the source surface, linking surfaces and target surface can be settled automatically. The virtual decomposition is applied to extract the sweepable part from the solid. Then, the sweepable part can be discretized by sweep method. If all of sub-domains are sweepable, the all-hexahedral mesh can be generated for the solid.
(4) A new conforming hybrid mesh generation method is proposed and applied to generate mesh for three-dimensional solids with open-ended tubular holes. A pyramidal element generation method is presented to solve the non-conforming problem. The regions around the tubular holes are presented by hexahedral elements. The tetrahedral mesh is generated to tessellate the rest of the domain. The pyramid elements are constructed at the interface between hexahedral and tetrahedral elements. High-quality hybrid mesh can be automatically created by the proposed method. Two kinds of special surface elements, tube element and triangular element with negative parts, are proposed for modeling solids containing many slender open-ended tubular shaped holes. The discretization of the surface is very simple by using these special elements, resulting in substantial savings in both data preparation and computing costs.
(5) The feature recognition method is applied to automatically determine the meshing algorithm for each solid of dams. And the mesh can be generated automatically by the presented methods. Thus, the whole dam can be meshed automatically without user interaction. The BFM is applied to predict the thermal evolution of dams during their construction with the generated mesh.
(1)为实现对复杂三维实体的网格自动生成,本文构建了一个三维网格生成框架。该框架分为网格数据管理、特征识别、虚拟分解和网格生成方法四个部分。本文设计了一个统一的数据管理器来管理网格数据,很好地实现了数据存储量和数据获取所需的计算量之间的平衡。统一的网格数据管理让程序的调整、维护和扩充十分便捷。在该框架中可以实现各种三维网格生成方法,可以将所得的网格单元转换为计算单元,并且可以导出到其他模块。
(2)为实现对复杂三维实体的四面体网格自动生成,本文提出了一种采用推进波前法生成域内点的Delaunay方法。该方法采用推进波前法来生成域内点,采用Delaunay内核将该点插入到网格中。本文加入了对前沿的识别,筛选出适合用来生成新点的前沿,剔除不满足要求的前沿,提高了算法的效率。该方法能够生成高质量的网格,具有较高的效率并且可以保证网格生成的收敛。
(3)为完成对复杂三维实体的六面体网格自动生成,本文提出了网格特征的概念,并构造了网格特征的识别方法。该方法能够从复杂三维实体中识别出可扫掠部分,并且可以自动识别出扫掠体的源面、目标面和连接面。然后采用虚拟体分解技术将可扫掠部分从实体中分解出来。分解得到的可扫掠子域可以采用扫掠法生成六面体网格。对分解得到子域全部可扫掠的情况,就可以实现六面体网格的自动生成。
(4)为实现了对含有细小管道的三维实体的网格自动生成,本文提出了一种混合网格自动生成方法。同时构造了一种五面体网格的生成方法来解决四面体网格和六面体网格之间的相容性问题。该方法在管道周围生成六面体网格,用四面体单元对剩余区域进行填充,采用金字塔五面体单元来连接这两种网格。该方法能够完成对含有细小管道的三维实体的高质量网格自动生成。为采用边界面法对含有细小管道的三维实体进行弹性力学分析,本文构造了管单元和含有空缺的三角形单元。采用这两种计算单元,降低了计算网格的生成难度,在提高了计算效率的同时有很高的计算精度。
(5)为了能够完成对混凝土坝的自动分析,采用本文的方法,通过特征识别,自动完成了对子域网格生成方法的判断,从而实现了对整个混凝土坝的三维网格自动生成。基于生成的网格,采用边界面法完成了对混凝土坝浇筑建造过程的模拟。
The boundary face method (BFM) based on the boundary integral equation (BIE) exhibits some extraordinary merits. Generally, the BFM only needs to discretize the boundary of the domain. And the mesh can be obtained by discretizing each piece wise continuous panel of the body's surface without restriction of element connectivity, hence, considerably simplifies the discretization task and the mesh generation method can be much more flexible. BFM also needs three-dimensional mesh to carry out the postprocess and analysis. The tetrahedral mesh can be generated automatically for complex solids. All-hexahedral meshes are preferred than tetrahedral mesh. But all-hexahedra meshing methods have proven to be more challenging. In order to discretize a complex solid, the volume needs to be decomposed manually, which is a time consuming and difficult task. Therefore, this dissertation conducts some useful researches and trials on the automatical three-dimensional mesh generation method for BFM. Based on the advantages of the BFM, some special elements are used to discretize the boudray of the domain. Hence, the discretization of the surface is very simple, resulting in substantial savings in both data preparation and computing costs. As a result, the following studies are carried out in this dissertation.
(1) In order to construct an automatical mesh generator, a program framework for three-dimensional mesh generation is developed. In the framework, some C++classes are designed to performing different tasks needed in overall mesh generation, such as mesh data management, feature recognition, virtual decomposition, and mesh generation methods. A mesh data manager is developed, the conflicting requirements of compactness and computational efficiency is well balanced. The uniform mesh database is convenient for modification, maintenance and expansion of the programme. A variety of three-dimensional mesh generation methods can be implemented in this framework. The resulting mesh cells can be converted into elements for analysis and dumped to postprocess module.
(2) A Delaunay method coupled with the advancing front method for automatical tetrahedral mesh generation is presented. The internal points are created by advancing front method and inserted into the mesh by Delaunay kernel procedure. To get better efficiency, a front identification and field point generation method is proposed and applied. The background mesh is used to specify mesh size distributions over arbitrarily shaped domains. The grid is applied to manage the background mesh, thus the point can be quickly located in the backgroud mesh. The mesh generation method combines the advantages of the high point placement quality of the advancing front method and the high efficiency and convergence guaranty of the Delaunay algorithm.
(3) The sweep method is applied to generate hexahedral mesh. The mesh feature recognition method is proposed to recognize the sweepable part from the complex solid. And the source surface, linking surfaces and target surface can be settled automatically. The virtual decomposition is applied to extract the sweepable part from the solid. Then, the sweepable part can be discretized by sweep method. If all of sub-domains are sweepable, the all-hexahedral mesh can be generated for the solid.
(4) A new conforming hybrid mesh generation method is proposed and applied to generate mesh for three-dimensional solids with open-ended tubular holes. A pyramidal element generation method is presented to solve the non-conforming problem. The regions around the tubular holes are presented by hexahedral elements. The tetrahedral mesh is generated to tessellate the rest of the domain. The pyramid elements are constructed at the interface between hexahedral and tetrahedral elements. High-quality hybrid mesh can be automatically created by the proposed method. Two kinds of special surface elements, tube element and triangular element with negative parts, are proposed for modeling solids containing many slender open-ended tubular shaped holes. The discretization of the surface is very simple by using these special elements, resulting in substantial savings in both data preparation and computing costs.
(5) The feature recognition method is applied to automatically determine the meshing algorithm for each solid of dams. And the mesh can be generated automatically by the presented methods. Thus, the whole dam can be meshed automatically without user interaction. The BFM is applied to predict the thermal evolution of dams during their construction with the generated mesh.
引文
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