三维空间非结构网格生成方法研究

随着计算流体力学领域待解决问题复杂程度的不断提高,传统的统一贴体结构网格已不能很好地满足针对复杂外形的高精度网格生成需求,而非结构网格以其独特优势受到CFD工作者的普遍关注。带有附面层的非结构网格是非结构网格生成的难点。进行了非结构四面体网格的生成方法研究,同时结合Spider软件平台中结构网格参数化附面层推进的技术优势,进行了基于Spider软件平台中非结构网格生成模块“UGCS”的开发。通过分析大量网格生成实例中网格质量和数值计算结果,验证了算法的可靠性与鲁棒性。     

A new adaptive grid generation by elliptic equations with orthogonality at all of the boundaries

A new adaptive grid generation procedure is proposed, which combines a previously developed method that used Anderson's adaptive grid scheme along with a method for controlling grid spacing and orthogonality on all of the boundaries. The proposed method assigns the desired grid stretching over the smooth region during initial grid system generation and before grid adaptation is performed. After properly interpreting the smoothing term of the weighting function, the desired grid stretching is added to the adaptive grid scheme. Several test cases illustrate the method's feasibility.     

Automatic hexahedral mesh generation for multi-domain composite models using a hybrid projective grid-based method

This paper presents an algorithm to generate an all-hexahedral mesh of a multi-domain solid model using a hybrid grid-based approach. This is based on a projective concept during the boundary adaptation of the initial mesh. In general, the algorithm involves the generation of a grid structure, which is superimposed on the solid model. This grid structure forms an initial mesh consisting of hexahedral elements, which intersect fully or partially with the solid model. This initial mesh is then shrunk in an outside-in manner to the faces of the model through a node projection process using the closest position approach. To match the resulting mesh to the edges of the model, a minimal deformation angle method is used. Finally, to match the vertices with the nodes on the mesh, a minimal warp angle method is employed. To create the mesh of a multi-domain solid model, an outside-in and inside-in hybrid of the grid-based method is used. This hybrid method ensures that the meshes of the different domains are conforming at their common boundary. This paper also describes two methods for resolving cases of degenerate elements: a splitting technique and a wedge insertion technique.     

四边形网格间接生成方法

研究了基于背景三角网格的四边形网格间接生成算法,并针对三角形合并过程中容易残留三角形的缺陷提出了确定侧边的详细算法,该算法主要是依据背景三角网格中边的位置和前沿边的情形,通过背景三角网格中已存在的边、边交换或边分割确定侧边,以避免在三角形合并过程中残留三角形单元。最后给出实例验证了算法的有效性。     

基于循环神经网络的正交网格的自动化生成算法

随着计算机图形学、工业设计、自然科学等领域的飞速发展,对高质量的科学计算方法的需求随之增大,而这些科学计算的方法离不开高质量的网格生成算法。对于常用的正交网格生成算法,是否能减少计算量以及是否能降低的人工干预等问题仍是它们所面临的主要挑战。针对这些挑战,对于单连通的目标区域,提出了基于循环神经网络之一的长短期记忆网络（LSTM）和Schwarz-Christoffel共形映射（SC映射）的正交网格自动化生成算法。首先,利用基于SC映射的Gridgen-c工具的基本条件将网格生成问题转换为一个带线性限制条件的整数规划问题。接着,利用预处理后的GADM数据集和LSTM训练获得能计算目标多边形区域每个顶点转角类型的概率的分类器。该分类器可以大幅度降低整数规划问题的时间复杂度,使该问题能被自动化且快速地求解。最后以简单图形区域、动画图形区域、地理边界区域为样例,进行网格生成实验。结果表明：对于简单图形区域,所提算法均能达到最优解;而对于具有复杂边界的动画图形区域和地理边界区域,实例网格结果表明,所提算法能使这些目标区域的计算量分别降低88.42%和91.16%,且能自动化地生成较好的正交网格。     

扫掠法有限元网格生成方法

为了提高有限元网格的生成质量,扫掠法生成六面体网格过程中内部节点定位成为关键一步,在研究复杂扫掠体六面体有限元网格生成算法过程中,提出了一种基于扫掠法的六面体网格生成算法,算法利用源曲面已经划分好的网格和连接曲面的结构化网格,用仿射映射逐层投影,生成目标曲面,提出基于Roca算法的内部节点定位的新算法,运用由外向内推进的波前法思想,生成全部的六面体网格。通过实例表明,该算法快速,稳定,可靠,可处理大量复杂2.5维实体六面体网格生成问题。     

边界简化与多目标优化相结合的高质量四边形网格生成

目的 高质量四边形网格生成是计算机辅助设计、等几何分析与图形学领域中一个富有挑战性的重要问题。针对这一问题,提出一种基于边界简化与多目标优化的高质量四边形网格生成新框架。方法 首先针对亏格非零的平面区域,提出一种将多连通区域转化为单连通区域的方法,可生成高质量的插入边界;其次,提出"可简化角度"和"可简化面积比率"两个阈值概念,从顶点夹角和顶点三角形面积入手,将给定的多边形边界简化为粗糙多边形;然后对边界简化得到的粗糙多边形进行子域分解,并确定每个子域内的网格顶点连接信息;最后提出四边形网格的均匀性和正交性度量目标函数,并通过多目标非线性优化技术确定网格内部顶点的几何位置。结果 在同样的离散边界下,本文方法与现有方法所生成的四边网格相比,所生成的四边网格顶点和单元总数目较少,网格单元质量基本类似,计算时间成本大致相同,但奇异点数目可减少70% 80%,衡量网格单元质量的比例雅克比值等相关指标均有所提高。结论 本文所提出的四边形网格生成方法能够有效减少网格中的奇异点数目,并可生成具有良好光滑性、均匀性和正交性的高质量四边形网格,非常适用于工程分析和动画仿真。     

Finite element mesh generation

The capabilities of a geometric modeller are extended towards finite element analysis by a mesh generator which extracts all its geometric and topological information from the model. A coarse mesh is created and subsequently refined to a suitable finite element mesh, which accomodates material properties, loadcase and analysis requirements. The mesh may be optimized by adaptive refinement, ie according to estimates of the discretization errors.A survey of research and development in geometric modelling and finite element analysis is presented, then an implementation of a mesh generator for 3D curvilinear and solid objects is described in detail.     

A strategy of automatic hexahedral mesh generation by using an improved whisker-weaving method with a surface mesh modification procedure

One of the demands for three dimensional (3D) finite element analyses is the development of an automatic hexahedral mesh generator. For this problem, several methods have been proposed by many researchers. However, reliable automatic hexahedral mesh generation has not been developed at present. In this paper, a new strategy of fully automatic hexahedral mesh generation is proposed. In this strategy, the prerequisite for generating a hexahedral mesh is a quadrilateral surface mesh. From the given surface mesh, combinatorial dual cycles (sheet loops for the whisker-weaving algorithm) are generated to produce a hexahedral mesh. Since generating a good quality hexahedral mesh does not depend only on the quality of quadrilaterals of the surface mesh but also on the quality of the sheet loops generated from it, a surface mesh modification method to remove self-intersections from sheet loops is developed. Next, an automatic hexahedral mesh generator by the improved whisker-weaving algorithm is developed in this paper. By creating elements and nodes on 3D real space during the weaving process, it becomes possible to generate a hexahedral mesh with fewer bad-quality elements. Several examples will be presented to show the validity of the proposed mesh generation strategy.     

非结构网格布点方法研究进展

用有限元方法求解偏微分方程初边值问题首先要离散求解区域,即网格生成,并且网格质量的好坏直接影响着有限元解的收敛性和精度,所以关于网格生成有很多学者从各自的领域出发做了大量的研究工作。论文关注于非结构网格点的布置方法,对已有的具有代表性的布点方法的研究进展进行了分类综述。     

Automatic mesh generation and modification techniques for mixed quadrilateral and hexahedral element meshes of non-manifold models

A typical geometric model usually consists of both solid sections and thin-walled sections. Through using a suitable dimensional reduction algorithm, the model can be reduced to a non-manifold model consisting of solid portions and two-dimensional portions which represent the mid-surfaces of the thin-walled sections. It is desirable to mesh the solid entities using three-dimensional elements and the surface entities using two-dimensional elements. This paper proposes a robust scheme to automatically generate such a mesh of mixed two-dimensional and three-dimensional elements. It also ensures that the mesh is conforming at the interface of the non-manifold geometries. Different classes of problems are identified and their corresponding solutions are presented.     

基于局域网的有限元网格分布式并行生成

在常见的PC＋Windows＋LAN环境下,采用Winsock API网络通信接口实现了局域网上的分布式并行有限元网格生成。网格生成区域在服务器上按照工作站数量被分解为若干个子区域,这些子区域及网格控制参数通过局域网（LAN）传给工作站。子区域在工作站上被剖分成子网格并通过局域网传回服务器以合并形成最终网格。算例表明只要有足够的计算节点,分布式并行技术可以将网格生成速度大幅度提高,而网络通信所占时间的比例基本固定。     

Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations

In this paper, we consider a singularly perturbed boundary-value problem for fourth-order ordinary differential equation (ODE) whose highest-order derivative is multiplied by a small perturbation parameter. To solve this ODE, we transform the differential equation into a coupled system of two singularly perturbed ODEs. The classical central difference scheme is used to discretize the system of ODEs on a nonuniform mesh which is generated by equidistribution of a positive monitor function. We have shown that the proposed technique provides first-order accuracy independent of the perturbation parameter. Numerical experiments are provided to validate the theoretical results.     

Adaptive discrete harmonic grid generation

We present a new adaptive-harmonic structured grid generation method. It is based on a functional that shares a common set of minimizers with Ivanenko’s harmonic functional [A.A. Charakhch’yan, S.A. Ivanenko, Curvilinear grids of convex quadrilaterals, Comput. Maths. Math. Phys. 28(2) (1988) 126–133.]. An unconstrained optimization process related to a continuation parameter is used to guarantee the convexity of the grid cells. Several numerical examples of grids generated on quite irregular 2D$2D$regions, show the effective performance of the proposed method and its robustness when preset monitor functions are given.     

三维有限差分计算中大规模网格生成及显示技术

针对爆炸与冲击问题并行仿真计算软件PMMIC-3D（Parallel Multi-Material in Cell 3D）的计算网格为正交六面体网格的特点,开发与PMMIC-3D接口统一的可对任意复杂三维实体模型进行大规模有限差分网格生成的三维前处理软件MESH-3D.MESH-3D采用CSG和STL模型两种建模方式进行复杂实体建模,并采用基于边的整体切片算法,借鉴计算机图形学中的扫描线填充算法完成三维有限差分网格划分.在绘制网格时,删除网格单元的公共面,大大缩短计算时间和减少存储空间,实现对网格的快速消隐显示.MESH-3D可实现百亿量级网格单元的生成和显示.三维前处理软件MESH-3D的开发有力地支持爆炸与冲击问题的仿真计算.     

Fully automatic and fast mesh size specification for unstructured mesh generation

A fully automatic surface mesh generation system is presented in this paper. The automation is achieved by an automatic determination of a consistent mesh size distribution, which is based on geometry rasterisation. The user specifies a minimal and maximal allowed mesh size, and a maximal allowed curvature angle for the complete geometry, or, rather, parts of it. Now, these local curvature and local characteristic lengths of the geometry are computed, which determine the local mesh size. These local mesh sizes are stored and smoothed in a Cartesian background mesh. Afterwards, the triangulation is generated by an advancing front triangulator: the local resolution of the surface triangulation is determined by the mesh sizes stored in the Cartesian background mesh. The object-oriented design and implementation is described. The complete system is very fast due to an efficient parallelisation based on MPI for computer systems with distributed memory.     

三角网格的自适应细分研究

提出面向三角网格全局细分和局部自适应的细分算法。在原三角网格模型上计算每个面片的中心坐标,据此生成的中心坐标点作为新的顶点坐标进行重新绘制得到三角基网格,然后进行多次迭代,达到基本的全局细分目标。在最后生成的基网格上,可以通过调节最大网格面积和平均网格面积之间的比例系数等,来得到更加均匀的三角网格。实验表明该方法能到得到质量较高的细分结果。     

基于大规模智能电网网格结构的查询方法

由于智能电网输电线路监测系统的查询多数是针对无线传感器网络(WSN)的全局式查询,不能满足用户基于任意区域的灵活高效的查询需求,根据该系统的网络布局和查询特点,提出了一种基于大规模智能电网网格结构的查询方法MSQuery。MSQuery将不同网格内的查询节点的数据汇聚到一棵或多棵逻辑查询树上, 采用逻辑查询树的合并策略建立优化的回收路径。将MSQuery与采用路线型结构进行查询的RSA算法和采用簇型结构进行查询的SkySensor算法进行对比,结果显示MSQuery的平均传输消耗最小,平均剩余能量最大。实验结果表明,MSQuery可以快速地返回查询窗口内的查询结果,降低通信消耗,节省传感器节点能量。