面向地学研究的六面体网格生成方法研究

发布时间：2018-06-11 22:56

本文选题：地学模拟 + 空间分析　；参考：《南京师范大学》2013年硕士论文

【摘要】：随着计算机技术和数值模拟计算方法的发展,目前进行地学机理与过程模拟的基本思路是对地理空间进行二三维有限元网格离散,然后采用相关数值计算方法完成计算模拟,故有限元网格是开展地学机理与过程模拟的基础。同时,有限元网格可支持缓冲区分析、叠加分析等传统GIS空间分析,由此可见,有限元网格在地学机理与过程模拟及传统GIS空间分析中扮演着十分重要的角色。三维有限元网格中,六面体网格在单元数量、自由度及计算精度等方面具有明显优势,已成为应用最广泛的三维网格之一,也是保证高效开展复杂地学研究的首选网格。然而,六面体网格生成一直是有限元等领域的难点,同时由于地学研究对象通常具有边界复杂、约束条件多等特点,针对地学研究对象的六面体网格生成问题仍未得到很好的解决,这导致六面体网格特别是非结构化六面体网格在地学研究中的应用尚且不足。为满足相关地学研究对六面体网格的需求,促进以数值计算方法为基础的地学模拟及传统GIS空间分析的进一步发展,本文开展了面向地学研究的六面体网格生成方法研究,针对常见地学实体模型,研究了三维空间对象的结构化与非结构化六面体网格生成,取得的主要成果如下： (1)结合地学研究对象自身特点,对传统栅格法进行扩展,基于地学研究实体表面模型(含约束条件),通过设计几何特征识别及约束处理机制,使其能顾及实体边界特征及内部约束点、约束线、约束面、约束洞等约束特征,在实体三维空间合理的生成高质量的六面体网格,提高传统栅格法边界拟合及约束处理能力,最后,采用网格质量优化算法提高网格生成质量。 (2)开展了基于Voronoi图的三维实体中轴生成研究,首先从三维实体中采样,然后计算采样点集的Voronoi图,最后利用两个与采样范围及密度无关的过滤条件从生成的Voronoi图中挑选出分布于实体中轴附近的Voronoi子集,实现三维实体中轴生成,为非结构化六面体网格生成算法做准备。 (3)结合传统栅格法及AFT法的算法优点,引入水平集方法思想,将地学实体表面三角网模型作为数据源,以结合距离场的各级水平(前沿水平等值面)作为向导,从内部种子开始,识别种子表面四边形网格特征,然后利用网格推进模板,在前沿水平等值面之间推进生成非结构化六面体网格,最后,通过网格质量优化算法确保网格质量。本文以南京南站区域地质体数据为实例进行验证,验证结果证明本文研究算法可靠有效,可对一般地学实体全自动进行六面体网格生成,在一定程度上满足地学机理与过程模拟分析及传统GIS空间分析对六面体网格的需求。
[Abstract]:With the development of computer technology and numerical simulation methods, the basic idea of geoscientific mechanism and process simulation is to discretize the geographical space with two-dimensional finite element mesh, and then complete the calculation simulation by using the relevant numerical calculation method. Therefore, finite element mesh is the basis of geoscientific mechanism and process simulation. At the same time, finite element mesh can support traditional GIS spatial analysis, such as buffer analysis and superposition analysis. It can be seen that finite element mesh plays a very important role in geoscientific mechanism and process simulation and traditional GIS spatial analysis. Hexahedron mesh is one of the most widely used three-dimensional meshes, which has obvious advantages in element number, degree of freedom and computational accuracy. It is also the first choice to ensure the efficient research of complex geology. However, the generation of hexahedron mesh has always been a difficult point in the field of finite element analysis. The problem of hexahedron mesh generation for geoscience research objects is still not well solved. As a result, the application of hexahedron mesh, especially unstructured hexahedron grid, in geoscience research is still insufficient. To promote the further development of geoscience simulation based on numerical calculation method and spatial analysis of traditional GIS, this paper develops the research of hexahedron mesh generation method for geoscience research, aiming at the common geoscientific entity model. In this paper, the structured and unstructured hexahedron mesh generation of 3D spatial objects is studied. The main results are as follows: (1) the traditional grid method is extended by combining the characteristics of geoscientific objects. Based on the geoscientific study of solid surface model (including constraint conditions), the geometric feature recognition and constraint processing mechanism are designed to make it take into account the entity boundary features, internal constraint points, constraint lines, constraint surfaces, constraint holes, and so on. The high quality hexahedron mesh is generated reasonably in the solid three-dimensional space to improve the traditional grid method boundary fitting and constraint processing ability. Finally, The mesh quality optimization algorithm is used to improve the quality of mesh generation. (2) the research of generating the central axis of 3D entity based on Voronoi diagram is carried out. Firstly, samples are sampled from 3D entity, then the Voronoi diagram of sampling point set is calculated. Finally, two filtering conditions independent of sampling range and density are used to select the Voronoi subset distributed near the axis of the entity from the generated Voronoi diagram to realize the generation of the three-dimensional solid axis. In order to prepare for the unstructured hexahedron mesh generation algorithm, combining the advantages of the traditional grid method and the AFT method, the level set method is introduced, and the geo-entity surface triangular network model is used as the data source. The quadrilateral mesh features of the seed surface are identified by combining the various levels of the distance field (the front level isosurface) as a guide, and then the mesh propulsion template is used to identify the quadrilateral mesh features of the seed surface. The unstructured hexahedron mesh is generated between the front level isosurface. Finally, the mesh quality is ensured by the mesh quality optimization algorithm. This paper takes the regional geological body data of Nanjing South Railway Station as an example to verify the grid quality. The results show that the algorithm is reliable and effective, and it can generate hexahedron mesh automatically for general geo-entities. To some extent, it can meet the requirements of geoscience mechanism and process simulation analysis and traditional GIS spatial analysis for hexahedron mesh.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：P208;TP391.7

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