具有大量椭圆颗粒/孔洞随机分布区域的计算机模拟及其改进三角形自动网格生成算法

针对颗粒／孔洞为椭圆形状并且呈随机分布的多相复合材料给出了一种计算机模拟方法，同时针对这样复杂的二维区域提供了一个改进的快速自动三角形网格剖分算法。最后用实例说明了算法的有效性。此算法可以推广到三维情形、裂纹材料等。     

脆性材料破坏模拟的网格生成算法

脆性材料的破坏过程具有随机性,当前的网格生成算法没有充分考虑脆性材料破坏时裂纹扩展和碎块生成的随机性。在Persson网格生成算法与Delaunay随机网格剖分理论基础上,提出了一种可根据模拟需要动态控制网格品质的网格生成算法。通过对随机分布点的Delauna三角化,生成初始网格,然后将网格体系比拟为桁架结构,网格节点即为桁架节点。桁架节点在虚拟力作用下可动态调整位置,并最终达到整个体系受力平衡。对Persson 算法中的尺寸分布函数和收敛条件进行了修正,从而提高了收敛速度,并适用于任意形状对象的网格剖分。 基于VC++平台开发了算法程序。通过实例对算法进行了验证,表明算法能够满足脆性材料破碎模拟的需要。     

一种三维表面网格自动生成方法

提出了一种改进的区域分解法,用于三维表面三角形和四边形网格的自动生成。基于区域分解法的三维表面网格生成的主要技术包括三维表面三角形面片拓扑关系的建立,表面三角形面片的分组及特征面的确定,空间曲线上网格节点的生成,区域内外边界的合并,最佳剖分面的确定,以及网格的光滑处理等。本文对这些技术进行了详细的介绍。本文提出的表面网格生成方法具有算法可靠、生成网格效率高以及生成网格质量高等优点。最后给出三维表面网格生成实例验证了本文提出方法的可靠性。     

网格自适应技术在复杂外形流场模拟中的应用

建立了一套适用于非结构混合网格自适应方法,针对激波和涡的不同特征采用不同加密探测器,各向异性加密棱柱单元并沿物面法向方向剖分所有棱柱层,各向异性剖分四面体单元,并保证四面体与棱柱交界面上网格协调。构造Hermit插值近似投影物面新加网格点和基于Laplacian光滑方法对空间网格进行优化。通过网格自适应加密,使用Roe格式计算高超声速球头绕流的红玉现象得到明显减轻。F16飞机含激波和脱体涡的流场自适应计算表明,网格加密集中在激波面和涡核附近区域,激波和涡计算更准确。     

一种新的准结构网格生成方法

在有限元分析中，高质量的结构网格可以有效地提高有限元分析的精度，但结构网格的几何适应性差，针对复杂边界的二维计算模型，现有的方法很难自动生成高质量的结构网格；而非结构网格几何适应性很好，但存在计算效率低和精度差等问题。提出了一种新的准结构网格生成方法，能够实现复杂区域的网格自动生成并且具有高网格质量。该方法首先对计算区域运用Delaunay三角剖分技术生成粗背景网格；然后利用背景网格，使用优化的Voronoi图生成过渡的蜂巢网格；最后，通过中心圆方法对蜂巢网格单元进行结构网格剖分。分析NACA0012翼型数值模拟结果表明，提出的新准结构网格生成方法能够对边界复杂的模型自动生成高质量的网格，并且通过三种不同拓扑类型网格计算结果相互对比及与实验结果对比，证明准结构网格具有高计算精度。     

面向复杂几何模型的并行四面体网格生成方法

面向大规模工程计算等数值模拟领域，提出了一种支持复杂几何模型的大规模四面体网格并行生成方法。该方法以复杂几何模型作为输入，首先采用串行网格生成方法生成初始四面体网格，然后通过两级区域分解方法将初始网格分解为多个子网格并分配到相应的进程中，进程间并行地提取出子网格的表面网格，并基于几何模型对面网格进行贴体加密，最后对加密后的面网格采用Delaunay方法重新生成四面体网格，该方法可以更好地适应高性能计算机体系结构，较好地克服了并行方法中并行性能和网格质量不能兼顾的问题。对三峡大坝模型进行测试和验证，证明该方法具有良好的并行效率和可扩展性，可以在数万处理器核上并行生成数十亿高质量四面体网格。     

复杂三维组合曲面的有限元网格生成方法

提出一种基于映射法的复杂三维组合曲面的有限元网格全自动生成方法。通过引入虚边界解决了闭合曲面在参数域中边界不完整的问题；通过调节虚边界提高了复杂组合曲面网格生成的质量。改进二维多边形区域的裁减算法，解决了闭合曲面在参数空间中的边界环形成问题。对曲面片公共边界进行统一离散化处理，以满足有限元网格的相容性要求。以边界表示(B—Rep)数据结构为基础，实现了组合曲面全自动网格剖分的总成算法．改进了曲面网格剖分布点算法，并结合局部连接、诊断交换等技术，优化了网格的整体质量。     

三维约束Delaunay三角化的边界恢复和薄元消除方法

提出一种有效的三维约束Delaunay三角剖分的边界恢复算法，该算法综合了P．L．George算法和N．P．Weatherill算法的优点，通过将约束边和约束面加以恢复，保持了实体边界的完整性，解决了经典Delaunay算法不能剖分凹域的问题，从而实现了复杂三维实体的网格剖分。提出了一种简易而有效的消除薄元方法——薄元分解法，彻底解决了三维Delaunay三角剖分过程中所产生的薄元问题。实践证明，本文提出的边界恢复算法和薄元消除算法健壮有效，生成网格的质量高，并且易于实现。     

六面体网格再划分过程中畸变和模具干涉单元的处理方法

针对金属体积成形过程中有限元网格畸变和再划分问题,研究了工件网格畸变单元中表面四边形面片分解为三角形面片时的重叠问题,提出了将工件与模具接触区域的工件三角形面片用模具表面三角形面片代替的算法,并给出了接触区域判断、相交点计算、相交三角形环的二次剖分以及融合拼接等关键技术,算法能够很好地描述工件与模具接触区域的形状特征,...     

薄元分解与Laplacian光顺相结合的四面体有限元网格优化方法

提出一种有效的三维实体四面体有限元网格质量优化方法以满足有限元分析对网格质量的要求。对薄元分解法进行改进,改进的薄元分解法更全面地考虑了各种劣质单元类型,能够对三维实体网格剖分中产生的各种类别的孤立劣质单元进行有效的分解;将改进的薄元分解法与Laplacian光顺优化方法相结合以解决某些网格剖分算法如推进波前法和Delaunay三角化方法产生的非孤立劣质单元问题。经过实例检验,本文提出的四面体单元网格优化算法健壮有效、易于实现,能够显著提高最差单元的质量。     

An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved.     

用逐点插入法生成Delaunay四面体自适应网格

介绍一种基于Delaunay算法的四面体自适应网格的自动划分方法。该方法用单元尺度场控制生成网格的疏密分布,在不满足尺度场要求的单元面形心处插入新节点,同时计算新节点单元尺寸参数,实现三维实体的Delaunay四面体自动划分。此方法具有几个特点:一是表面网格与体内网格同步划分,无需区分两者;二是结点与单元同时生成;三是生成网格自适应性好,疏密分布任意。另外,还介绍了三维网格划分中两个相关算法:一个是约束面恢复算法,该算法基于约束面不允许有单元边与之相交的性质而提出的;另一个是将二维射线法推广至三维空间,判断一个点是否在一多面体内,实现了凹多面体的划分。最后通过算例对单元质量进行了评价。本文所述方法是一种有效的四面体自适应单元生成算法。     

一种基于双前沿推进的边界层网格生成算法

高雷诺数粘性流动模拟对边界层内的网格正交性有特殊要求.对于复杂外形,这类问题的网格自动化生成十分困难.面向该问题,提出一种双前沿推进思想,并形成一种面向复杂几何外形的边界层网格全自动生成算法.结合多种网格技术处理局部几何特征以保证边界层网格的质量.双前沿推进思想同时适用于多块结构网格和混合网格的边界层网格生成.多个模型...     

FCC晶体中不均匀变形对空洞长大的影响

通过编制率相关有限元用户子程序,采用一个单胞模型研究了FCC晶体中孔洞在单晶及晶界的长大行为,分析了由于晶体取向及变形失配对孔洞长大和聚合的影响。研究结果表明：孔洞的形状和长大方向与晶体取向密切相关;晶界上孔洞的长大速度大于单晶中孔洞的长大速度;晶粒间的变形失配加速了晶界上孔洞的长大趋势,因而使材料易发生沿晶断裂,随着晶粒间取向因子差异的增加,孔洞越易沿着晶界长大。     

A parallel unstructured dynamic mesh adaptation algorithm for 3‐D unsteady flows

An unstructured dynamic mesh adaptation and load balancing algorithm has been developed for the efficient simulation of three‐dimensional unsteady inviscid flows on parallel machines. The numerical scheme was based on a cell‐centred finite‐volume method and the Roe's flux‐difference splitting. Second‐order accuracy was achieved in time by using an implicit Jacobi/Gauss–Seidel iteration. The resolution of time‐dependent solutions was enhanced by adopting an h‐refinement/coarsening algorithm. Parallelization and load balancing were concurrently achieved on the adaptive dynamic meshes for computational speed‐up and efficient memory redistribution. A new tree data structure for boundary faces was developed for the continuous transfer of the communication data across the parallel subdomain boundary. The parallel efficiency was validated by applying the present method to an unsteady shock‐tube problem. The flows around oscillating NACA0012 wing and F‐5 wing were also calculated for the numerical verification of the present dynamic mesh adaptation and load balancing algorithm. Copyright © 2005 John Wiley & Sons, Ltd.     

平面区域四边形网格自动生成技术

本文分析和综述了四边形网格自动生成的各种算法,给出了三角形网格向四边形网格转换的局部算法,以及有FCT思想直接生成四边形和三角形网格算法。详细分析了此法之下生成网格的几何拓朴性质,最后给出实例验证了算法的有效性。     

A stable and accurate projection method on a locally refined staggered mesh

In this paper, a robust projection method on a locally refined mesh is proposed for two‐ and three‐dimensional viscous incompressible flows. The proposed method is robust not only when the interface between two meshes is located in a smooth flow region but also when the interface is located in a flow region with large gradients and/or strong unsteadiness. In numerical simulations, a locally refined mesh saves many grid points in regions of relatively small gradients compared with a uniform mesh. For efficiency and ease of implementation, we consider a two‐level blocked structure, for which both of the coarse and fine meshes are uniform Cartesian ones individually. Unfortunately, the introduction of the two‐level blocked mesh results in an important but difficult issue: coupling of the coarse and fine meshes. In this paper, by properly addressing the issue of the coupling, we propose a stable and accurate projection method on a locally refined staggered mesh for both two‐ and three‐dimensional viscous incompressible flows. The proposed projection method is based on two principles: the linear interpolation technique and the consistent discretization of both sides of the pressure Poisson equation. The proposed algorithm is straightforward owing to the linear interpolation technique, is stable and accurate, is easy to extend from two‐ to three‐dimensional flows, and is valid even when flows with large gradients cross the interface between the two meshes. The resulting pressure Poisson equation is non‐symmetric on a locally refined mesh. The numerical results for a series of exact solutions for 2D and 3D viscous incompressible flows verify the stability and accuracy of the proposed projection method. The method is also applied to some challenging problems, including turbulent flows around particles, flows induced by impulsively started/stopped particles, and flows induced by particles near solid walls, to test the stability and accuracy. Copyright © 2010 John Wiley & Sons, Ltd.     

四面体单元网格加密过程中的曲面逼近算法及程序实现

本文介绍了一种在四面体单元网格的加密过程中实现曲面逼近的算法．单元加密采用了最长边加密算法．曲面逼近实现了对二次曲面的逼近功能．当加密点所在边是边界面上的边时，将该点挪到对应的边界面上．挪动时根据该边所参与的两个边界三角形面的法向方向来确定加密点的挪动方向，再结合二次曲面方程来计算出挪动后点的新坐标．算例表明，对于由二次曲面边界围成的物体，这种算法能够有效地实现网格加密过程中的曲面边界逼近功能．     

Microstructure damage at ensemble of points for grain composites

Fracture concentration zones are considered in microstructure elements of grain composites. Mathematical model of micro-heterogeneous medium with random properties of elements is used for calculations. The distribution laws for the modules of elasticity and ultimate strengths in the elements as well as the tensor of macroscopic deformations for the composite serve as the initial data. Different types of stresses are evaluated. Correlation functions for micro stresses are obtained by the Green’s tensor method.Random microstructure strength condition is a difference between the stress and the ultimate strength at any point of an ensemble with a particular configuration. The probability of simultaneously exceeding the ultimate strength in this set of elements determines the likelihood of failure of this ensemble of points and the relative damage at the micro level.The damage is calculated using multivariate normal distribution. Structure of correlation matrix of distribution depends on the type of fracture concentration zones. Correlation functions of microstructure strength condition depend on the distance between the points of the ensemble. Calculations of multipoint damage are provided for several configurations of points, in particular, for the three points on a straight line segment, and for the five points in the vertices and the center of a tetrahedron. For two-dimensional distribution density, the smoothing surface formulas are derived, taking into account the moments of stresses up to and including the fourth order.The influence of microstructure properties and the type of ensemble of points on composite damage is demonstrated. Study of microstructure damage enables the prediction of early stages of construction material failure.