Shape Functions for Velocity Interpolation in General Hexahedral Cells

Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy's law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the L ² norm in the presence and absence of singularities, respectively.     

Velocity interpolation and streamline tracing on irregular geometries

Streamline tracing on irregular grids requires reliable interpolation of velocity fields. We propose a new method for direct streamline tracing on polygon and polytope cells. While some numerical methods provide a basis function that can be used for interpolation, other methods provide only the fluxes at the faces of the elements. We introduce the concept of full- and raw-field methods. Full-field methods have built-in interpolation but are often not defined on general grids such as polygonal and polyhedral grids which we examine here. Also, reliability issues may arise on non-simplicial meshes in terms of not being able to reproduce constant velocity fields. We propose an interpolation in H(div) and H(curl) valid on general grids that is based on barycentric coordinates and that reproduces uniform flow. The interpolation can be used to compute the streamline directly on the complex cell geometry. The method generalizes to convex polytopes in 3D, with a restriction on the polytope topology near corners that is shown to be satisfied by several popular grid types. Numerical results confirm that the method is applicable to general grids and preserves uniform flow.     

FEM Data Generator

The FEM data generator presented in this paper is used to generate quasi-automatically or automatically the basic data for 3-d or 2-d finite element analysis of engineering projects, such as element nodal connections, material parameters, nodal coordinates, restrained boundary conditions, and the information of applied load. With the symbol-identified input data system and the concept of interpolation function of isoperimetric element, this data generator deals with regular meshes, irregular meshes, and their arbitrary combination in unified routine and the same way to input data, which is available to any kind of elements and convenient to users. The work principle of this data generator and the features of corresponding computer routines are described in detail.     

An irregular triangle mesh buffer analysis method for boundary representation geological object in three-dimension

Three-dimensional (3D) buffer analysis is a basic function of spatial analysis used widely in 3D Geographic Information Systems (3DGIS). Current buffer analysis methods for spatial points and curves generally function well. One exception is buffer zone of surface. Previous researchers in this field have used voxel models to overcome this limitation; however, defects with voxel model buffer analysis include redundancies, approximations, and poor visualization characteristics. In this contribution, a surface buffer analysis method is presented for the boundary representation of geological objects. Exact geometric representation is achieved via the construction of irregular triangle meshes in 3D. The results can be used for 3D structural modeling and then form the basis for spatial analysis or model-based quantitative assessment in mineral potential mapping and resource evaluation. Three comparisons between existing voxel methods and our new method, evaluating visualization, precision and redundancy, are conducted. The comparisons show that our proposed method is robust and provides a higher quality output than voxel modeling. Finally, uncertainty analysis of buffer distance in different geological objects was discussed.     

有限单元法数据生成器

本文介绍有限单元法数据生成器采用字符标识的输入数据系统和等参元插值函数的概念,人工准自动或全自动生成实际工程问题二维或三维有限元分析所需要的基本数据,如单元节点号、材料参数、节点坐标、边界条件和荷载信息等等。这个数据生成器以统一的程序和相同的输入方式来处理规则网格、不规则网格,以及它们的任意组合和各种类型的单元,便于用户的使用。     

城市暴雨内涝数学模型的研究与应用

以城市地表与明渠、河道水流运动为主要模拟对象,研制了模拟城市暴雨内涝积水的数学模型。模型以平面二维非恒定流的基本方程和无结构不规则网格划分技术为骨架,同时,针对小于离散网格尺度的河道或明渠,应用了一维非恒定流方程的算法。采用分类简化处理的方法,将通道分为河道型、路面型、特殊通道型(城市内的二级河道),根据不同类型简化动量方程,求任意网格各个通道上的单宽流量。采用一维非恒定流方程模拟地下排水管网内的水流,并给出泵站、闸门、淹没出流管道等排水系统的处理方法。根据无结构不规则网格的设计思路,按照天津、南京、南昌三市的地形地貌特征分别设计多边形的计算网格。介绍了城市面雨量的计算方法以及数学模型在天津市、南京市、南昌市的应用情况和误差分析。     

Application of Multifocusing Method for an Irregular Topography Imaging

INTRODUCTION Astackofrecordedseismicdatabecomesoneof themainstepsinmoderndataprocessingwhenmulti foldacquisitionsystemsaretheleadingmethodof collectingseismicdata.Inthestackprocedure,the crucialoperationistimecorrection.Anaccurateand reliabletraveltimemoveoutcorrectionformulaisnec essaryinordertodostackproperly(Gelchinskyet al.,1999a).Themostfamousmoveoutexpressionis thenormalanddipmoveout(NMO/DMO)designed todescribethetraveltimeofprimaryreflectionsof common midpoint(CMP)data.Beingdes…     

基于TIN的三维地层建模及可视化技术研究

基于多层格网模型的表面建模方法,以及以此为基础形成的类三棱柱体元建模方法,要产生大量冗余的三角形面片或者细长的三棱柱单元,既不利于三维模型的快速浏览,也不能满足数值计算单元剖分的原则。采用TIN（不规则三角网）来表达地层面模型可以消除数据冗余。根据数据源的特点,实现了直接通过逐点插入法构造TIN模型,或者先通过Kriging插值法构造格网模型,再转化为TIN模型,以及利用等高线数据构造TIN模型。对TIN的裁剪算法进行了探讨,实现了地层面裁剪和断层的三维建模技术。借助可视化开发类库VTK,实现了三维地层模型的多种可视化表达方法。根据龙滩水电工程地质勘查情况,建立了坝址区域的三维地层模型。     

试验模型位移场中的几种光学测量方法比较

详细地分析了几种光学测试方法在模型试验中的使用情况。自动网格法在模型表面布置网格点容易,由于开挖或裂缝等原因去掉网格点,改进后的程序仍能自动编码,必要时可通过人机对话手工编码。散斑互相关法,在模型表面布置散斑较容易,改进后的程序在开挖情况下也能自动处理,但在散斑场遭受严重破坏情况下无法比较相关性。其他光学测试技术由于受试验条件的限制,而不适合使用。     

地下矿山裂隙岩体结构均质区三维划分方法研究

针对现有岩体结构均质区划分方法应用于地下矿山时存在细节辨识能力偏弱等问题,开展地下矿山岩体结构均质区三维精确划分方法研究。以广西铜坑矿锌多金属矿体3^#矿块为例,从岩体空间结构展布特性出发,构建由确定性与随机性结构面耦合的裂隙岩体三维模型;将岩体模型正交网格离散化,并选取模型网格子区的块体化程度值为均质区划分判据;利用K-means算法衡量不同数据源(网格)的相似性,结合误差平方和(SSE)度量聚类质量;最后重构三维岩体结构均质区,形成了一种地下矿山岩体结构均质区三维划分方法。研究成果表明:利用该方法能够从三维角度精确划分地下矿山岩体结构均质区,可为后续岩体质量评价及岩体离散元模拟的模型构建等工作提供有益参考。     

Algebraic multigrid techniques for discontinuous Galerkin methods with varying polynomial order

We present a parallel algebraic multigrid (AMG) algorithm for the implicit solution of the Darcy problem discretized by the discontinuous Galerkin (DG) method that scales optimally for regular and irregular meshes. The main idea centers on recasting the preconditioning problem so that existing AMG solvers for nodal lower order finite elements can be leveraged. This is accomplished by a transformation operator which maps the solution from a Lagrange basis representation to a Legendre basis representation. While this mapping function must be user supplied, we demonstrate how easily it can be constructed for somepopular finite element representations includingquadrilateral/hexahedral and triangular/tetrahedral DG formulations. Furthermore, we show that the mapping does not depend on the Jacobian transformation between reference and physical space and so it can be constructed with very limited mesh information. Parallel performance studies demonstrate the versatility of this approach.     

Adaption of polygonal strain markers

Two methods are presented whereby finite-strain data may be determined from naturally occurring irregular strain markers (polygons) which are of unknown pre-deformation shape and distribution, without assumptions as to the orientation of the finite-strain ellipse. The first method describes “construction” of ellipses within the polygons, these ellipses providing the basis for analysis by already developed techniques. The second method is a simple extension of Wellman's method, which graphically establishes a strain ellipse from angle and line data.     

基于三角单元外心下的幂率格式在丁坝绕流中的应用

针对在非结构网格水流数值计算,将各变量储存在三角单元外心进行离散,从而避免了由于非结构网格的非正交性而使用各种校正方法所带来的校正误差.采用Rhie-Chow的动量插值思想推导出基于SIMPLE意义下的水位校正方程,并详细给出了水位校正方程的离散形式.动量方程采用数值性能优良的幂率格式.计算结果成功地模拟出丁坝上、下游涡的特征量及流场情况,与水槽试验的资料吻合良好.     

钻井船插桩对邻近桩影响的耦合欧拉-拉格朗日有限元方法研究

依据模拟钻井船在黏土层中插桩对邻近桩影响的离心模型试验结果,研究了通过耦合欧拉-拉格朗日（CEL）有限元计算并结合非线性地基梁有限元计算,分析钻井船插桩对邻近桩影响问题的可行性。CEL有限元方法将产生大变形的土体设为欧拉体,采用欧拉有限元方法计算该区域的变形响应,计算过程中,欧拉体的空间网格形状、大小位置保持不变,物质可在网格之间运动;其他土体设为拉格朗日体,采用拉格朗日有限元方法计算变形响应,计算过程中,物质的运动和网格的变形保持一致。运用罚函数方法实现欧拉体与拉格朗日体的耦合。通过CEL有限元计算,可以确定钻井船插桩导致的邻近桩桩身水平位移。进一步通过非线性地基梁有限元模型计算确定桩身弯矩。计算结果表明,利用CEL有限元方法并结合非线性地基梁有限元方法计算出的桩身位移和弯矩沿桩长的变化与离心模型试验结果基本一致。说明采用CEL有限元方法并结合非线性地基梁有限元方法分析黏土层中插桩对邻近桩的影响问题是可行的。CEL有限元模型中欧拉土体范围的设置对计算结果有明显影响。研究表明,若插桩深度小于0.75倍桩靴直径,可将欧拉土体范围设置成1.00～1.25倍桩靴直径;若插桩深度大于0.75倍桩靴直径,将欧拉土体范围取为插桩深度以下0.5倍桩靴直径是恰当的。     

Kinematic (or hour-glass) mode control for a uniform strain quadrilateral by an assumed strain technique

Finite element and finite difference solid mechanics computer programs have often been observed to overestimate the stiffness of an elastic beam or the collapse load in elasto-plastic problems. There are a number of ways of overcoming these difficulties but many lead to unwanted degrees of freedom in the mesh which continuously degrade the solution if the errors are allowed to accumulate. These unwanted distortions are referred to as spurious or hour-glass modes, and special measures have to be taken if accurate predictions are to be achieved without their appearance. In this paper a new scheme based on assumed strains at the element level is described in the context of a two-dimensional, explicit, finite difference program. The scheme is compared with an earlier solution to this problem and is shown to have some advantages, particularly when irregular meshes and/or large deformations are encountered. Thorough testing indicates that the new formulation passes the patch test and leads to accurate predictions of bending stiffnesses and plastic collapse loads. An underlying consideration of the development was that the new scheme should be applicable to three-dimensional calculations. Although this has not been tested numerically, the extension to three dimensions is discussed.     

沉积地层系统三维实体模型构建方法

全面系统地研究了沉积地层系统三维实体构模的原理、方法及实施过程。针对沉积地层系统的几何结构特征,提出了一种基于钻孔数据的三维实体模型生成方法“钻孔-层面-实体法”。该方法首先使用二分拓扑结构将钻孔数据离散化为一系列散点,基于这些散点插值拟合出各个地层顶、底界面的初始高程,自动推算出缺失地层的地质成因;然后按照不同的地质成因,自动对缺失地层及其控制界面进行交切处理、高程调整与一致性处理;最后生成用三维块体或三棱柱体元充填的三维实体模型。通过上海城建工程中的一个应用实例验证了“钻孔-层面-实体法”的有效性。     

塑料板排水预压法加固软基效果分析

根据欲加固软基特点,采用塑料板排水预压法对其进行加固处理,通过合理安排施工顺序、布设排水系统和监测系统,现场监测及检测资料分析证明软基排水固结效果良好,达到了设计要求。     

具有守恒特性的二维溃坝洪水演进数值模型

基于结构网格,采用有限体积法建立了二维水动力学模型,模拟溃坝洪水在复杂实际地形条件下的流动过程。该模型采用中心迎风格式求解界面通量,并结合对界面变量的线性重构,使其具有空间上的二阶精度。分别采用中心差分方法和半隐式方法对底床坡度项和摩擦阻力项进行离散,保证了模型的和谐性和稳定性。对于复杂地形条件下溃坝洪水的模拟,负水深的产生是影响模型稳定的关键因素。当库朗特数小于0.25时,模型能够保证任何时刻的计算水深都是非负的,而无需对负水深单元进行特殊处理。因此,相比于现有的大部分溃坝洪水模型,该模型具有更强的鲁棒性和稳定性。     

去噪技术在地震资料处理中的应用

讨论了目前提高地震资料信噪比的方法及应用技术。通过对原始地震记录中普遍存在的噪声进行了分析。对于无规则噪声，应采用f-x域随机噪声衰减或多项式拟合的办法；对于有规则噪声，倾角滤波或FK滤波手段则更为有效。强调了在去噪过程中选择去噪参数的重要性。阐明了同相叠加技术也是一种提高地震资料信噪比的有效手段。总之。针对不同的噪声，应采用不同的去噪方法。实际地震资料处理表明，上述几种去噪方法对提高地震资料的信噪比是行之有效的。