求解潜水含水层剖面二维稳定流问题探讨

本文在对现有求解潜水含水层剖面二维流的多种方法及其特点进行分析的基础上,探讨新的求解方法.提出的方法只需进行一次网格剖分,在网格节点编号保持不变的情况下,把潜水面与单元相交的形状概化为五边形、任意四边形和三角形,按五边形、任意四边形和三角形子程序准确地求出潜水面穿越的单元的渗透矩阵.同时不用计算完全在潜水面之上的单元的渗透矩阵.本文给出具体的思路、算法步骤,计算潜水面的位置,通过比较数值解与解析解,两者虽然存在一定的误差,但是该方法总体结果是比较令人满意的.     

复杂区域四边形网格生成的一种改进方法

提出了一种改进的四边形网格生成算法。该法在行波法生成平面三角形网格的基础上，将一个三角形单元分解为三个四边形单元。经过优化处理，获得优良的计算域四边形网格。针对岩土工程结构问题，还提出了网格剖分中尖灭不连续面和锚杆及锚索的处理方案。地下洞室和边坡算例表明了这种方法的可行性和可靠性。     

电法测井的三维有限元模拟

研究了不同测量方式(井-地,地-井,井-井)下点源场井中电法的三维有限元数值模拟。考虑到深度方向上大范围的网格剖分和井眼的影响及井-井测量等因素,采用放射状三棱柱单元的网格剖分方式,以提高网格质量,减少剖分单元数;给出了三棱柱单元的坐标变换公式,进行精确的单元积分,减少了单元积分时间;结合非结构化网格技术,实现了复杂模型的模拟;开发出相应的程序实现了复杂条件下(如考虑井眼影响、井井测量、倾斜井情形、地形起伏等)电法测井的三维有限元模拟,数值算例验证了方法的可靠性及计算效率,并对不同情形下的异常响应进行了分析,为进一步的反演工作奠定了基础。     

三维地层的三棱柱剖分与土方计算

三维地层剖分算法是实现地层三维可视化与土方计算的重要基础。采用三棱柱体建模方法构造三维地层,分析任意平面切割三棱柱的不同情形,得出了针对三棱柱地层的剖分算法;提出了以切割面为分界面,将单个三棱柱剖分成多个小三棱柱的三角投影分割法--将三棱柱顶面、底面及切割截面按一定规则进行合理三角化划分,使划分后三角形在水平面上的投影相重合;将该3层三角形组合成以切割面为分界面的2层小三棱柱,从而完成剖分。土方计算中首先给出开挖体的边界控制方程,根据该控制方程所限定的内边界得到开挖区域,结合上述剖分算法,对该区域内所有小三棱柱体积求和,得到开挖土方量。将以上算法应用到广东省某重大水利工程中,实现了基坑模拟开挖及其土方计算。     

适合地形起伏的二维有限单元数值模拟技术

在有限单元法矩形～三角形单元剖分的基础上,提出了适合复杂地形条件下的网格剖分方法:平行四边形～三角形剖分方法。计算结果表明,该方法具有快速、高效的特点。只要对原有程序稍加修改,即可实现对复杂地形条件下的复杂地电断面进行自动剖分和网格节点自动编号。因此,对于复杂地形条件下的地电模型,该方法能快速地实现较为精确的数值模拟。     

基于非结构网格的带地形MT二维Occam反演及应用

本文对基于自适应非结构三角形网格的带地形MT数据二维Occam反演进行应用研究.自适应非结构三角形网格能够准确地模拟起伏地形和复杂地质构造,正演网格由有限元解的后验误差估计指导自动细化,保证了模型响应的准确性,反演网格在反演目标区域采用精细网格剖分,在模型边界区域采用粗网格剖分,在满足反演精度的前提下减少了不必要的反演...     

一种电磁法三维数值模拟的建模与网格剖分方法

为满足电磁法三维数值模拟解释对交互建模与可视化网格剖分的需求,利用计算机图形学、人机交互、拓扑关系学等技术,设计了起伏地形下三维矢量交互建模、四面体和六面体网格剖分流程,并开发了软件模块。该软件可提供起伏地形下电磁法三维数值模拟的四面体、六面体网格剖分的实用化工具,提高了电磁法三维在数据模拟与解释方面的可视化程度和计算效率。     

三角剖分自动生成的两种算法

网格剖分是数值模拟中有限元方法的基础和关键之一 ,剖分的好坏直接影响模拟结果的精度。数值模拟目前已应用于许多领域 ,如地球化学、水文地质、工程地质、矿床地质、油气地质、油藏工程、土力学和岩石力学等。在众多的网格剖分中 ,三角剖分最具优势 ,可以很好的拟合任意形状的边界 ;三角平面的组合可以较好地逼近任意曲面 ;三角形元素的局部逼近多项式可以采用完全多项式。以往三角剖分多采用手工剖分或者设计复杂的自动剖分 ,具有速度慢、扩大误差、增加计算周期和不能充分拟合边界等缺点。笔者在工作中发现了两种三角剖分自动生成方法—…     

基于GIS的河道贴体网格自动生成算法研究

利用地理信息系统(GIS)基于空间位置信息的技术特点,对河道贴体网格的自动化生成算法进行了研究。基于GIS矢量线的节点间空间位置关系,对任意位置上的河道流向进行了较高精度的数值表达,进而实现了河道断面的自动剖分;设计出一系列算法,解决了网格生成过程中可能出现的交叉、拧绕等问题,从而保证了剖分网格对河道区域平面分布的自适应性特征;基于数字高程模型(DEM)高程插值,对河道区域地表模型进行重建与分析,生成得到的河道贴体网格。经验证,该算法具有较好的贴体性质和较高的运算效率。     

一种适用于电磁法数值模拟的二维建模与网格剖分方法

为满足电磁法二维数值模拟解释对交互建模与可视化网格剖分的需求,利用计算机图形学、人机交互、拓扑关系学等技术,设计了基于测线、测点等信息的二维矢量建模、四边形和三角形网格剖分方法与流程,并开发形成了软件模块。该方法与软件可提供起伏地形下大地电磁、可控源音频大地电磁法二维数值模拟的三角形、四边形网格(下边界随地形变化或平地形)剖分实用化工具。将该方法应用到多种模型试验中,取得了良好的建模与网格剖分效果。     

复杂区域三维有限元四面体网格自动生成研究

基于经典三维Delaunay四面体网格的生成算法,介绍了一种三维约束Delaunay三角化网格划分算法,通过对约束的恢复和局部退化的消除,保证了边界的一致性和网格的惟一性,实现了三维约束区域的四面体网格自动生成;通过对四面体的外接球半径与其最短边长度的比值（记为a）和四面体体积与其外接球体积的比值（记为n）的控制,避免质量不佳的单元,使生成的网格达到预期的质量要求,并提出了一种a和n的计算方法,简化了质量参数的计算过程;对几何形状复杂,特别是含有薄层的实体,可通过在实体上增加约束来提高网格的质量和缩短计算时间,使该方法能够实现岩土工程中不同地质条件下的复杂区域的三维有限元网格自动生成,并且能够保证生成的网格质量较好,为高精度的有限元计算提供了充分条件。计算实例表明,该算法能够将复杂三维实体剖分成质量较好的Delaunay四面体网格,可有效地应用于工程中有限元网格的生成。     

Determination of volume and centroid of irregular blocks by a simplex integration approach for use in discontinuous numerical methods

Conventional integration techniques employed in continuous numerical methods can only be applied to regular blocks such as tetrahedrons or cubes. Therefore using such methods to compute the volume and centroid of blocks restricts the application of discontinuous numerical methods to the analysis of blocky systems. Subdividing a block into sub-blocks may solve this problem, but an algorithm which can be applied to blocks of different shapes has not been introduced. A new procedure for computing the volume and centroid of an arbitrarily shaped block based on area calculation using two-dimensional simplex integration and formulations of three-dimensional simplex integration developed by Shi is introduced in this paper. The new algorithm is easy to program and can be used instead of the complicated and time-consuming mesh generation approach. The proposed algorithm was programmed using VC?+?+?and is verified using an illustrative example.     

三维距离势离散单元法

通过定义距离势函数,提出一种适用于空间任意凸多面体单元的三维距离势函数离散单元法。该方法采用归一化的计算方式,将势函数表征为接触体间的距离函数,并基于此建立接触力计算方程,明确了势函数的物理意义,使接触力计算更加合理,无需对各种可能的接触形式进行差异化处理。新方法克服了原有势函数物理意义不明、接触力计算受单元形式影响等重要缺陷,并突破了四面体单元的限制,可采用空间任意凸多面体单元。通过若干算例说明新方法的正确性和有效性。数值模拟结果表明新方法能够很好处理空间任意多面体单元复杂接触变换过程,准确处理复杂非连续介质的运动过程。     

渗流问题的三维h型自适应有限元法研究

研究了三维渗流的自适应有限元法,建立了集成网格自动剖分、渗流有限元分析、网格调整、后处理等四大模块的四面体单元h型自适应系统。给出的算例证实了系统的有效性和优越性。     

Indirect unstructured hex-dominant mesh generation using tetrahedra recombination

Corner-point gridding is widely used in reservoir and basin modeling but generally yields approximations in the representation of geological interfaces. This paper introduces an indirect method to generate a hex-dominant mesh conformal to 3D geological surfaces and well paths suitable for finite-element and control-volume finite-element simulations. By indirect, we mean that the method first generates an unstructured tetrahedral mesh whose tetrahedra are then merged into primitives (hexahedra, prisms, and pyramids). More specifically, we focus on determining the optimal set of primitives that can be recombined from a given tetrahedral mesh. First, we detect in the tetrahedral mesh all the feasible volumetric primitives using a pattern-matching algorithm (Meshkat and Talmor Int. J. Numer. Meth. Eng. 49(1-2), 17–30 2000) that we re-visit and extend with configurations that account for degenerated tetrahedra (slivers). Then, we observe that selecting the optimal set of primitives among the feasible ones can be formalized as a maximum weighted independent set problem (Bomze et al. 1999), known to be \(\mathcal {N}\mathcal {P}\)-Complete. We propose several heuristic optimizations to find a reasonable set of primitives in a practical time. All the tetrahedra of each selected primitive are then merged to build the final unstructured hex-dominant mesh. This method is demonstrated on 3D geological models including a faulted and folded model and a discrete fracture network.     

New point-to-face contact algorithm for 3-D contact problems using the augmented Lagrangian method in 3-D DDA

This paper presents a new point-to-face contact algorithm for contacts between two polyhedrons with planar boundaries. A new discrete numerical method called three-dimensional discontinuous deformation analysis (3-D DDA) is used and formulations of normal contact submatrices based on the proposed algorithm are derived. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. This approach does not need to use an iterative algorithm in each time step to obtain the contact plane, unlike the ‘Common-Plane’ method applied in the existing 3-D DDA. In the present 3-D DDA method, block contact constraints are enforced using the penalty method. This approach is quite simple, but may lead to inaccuracies that may be large for small values of the penalty number. The penalty method also creates block contact overlap, which violates the physical constraints of the problem. These limitations are overcome by using the augmented Lagrangian method that is used for normal contacts in this research. This point-to-face contact model has been programmed and some illustrative examples are provided to demonstrate the new contact rule between two blocks. A comparison between results obtained by using the augmented Lagrangian method and the penalty method is presented as well.     

An automatic quadrilateral mesh generation algorithm applied to 2-D overland flow simulations

This paper presents an automatic quadrilateral mesh generation algorithm to provide 2-D meshes for simulating overland flow and transport problems in watershed systems. The conformal mapping method is studied deeply and specific treatment strategies are established according to the width of rivers and the area of other water storage zones. A conformity treatment method is proposed to deal with the incompatibility problems during discretizing the complex geometry with a plurality of sub-domains. This method ensures grid conformity through removing certain overlapped nodes and creating new appropriate nodes on common boundaries of the multi-domain mesh. Aiming at the undesired deviation of mesh boundaries from geometric contours, a relative position-percent interpolation method is proposed and a supplementary match method related to dead ends is presented. And, the double effects of projection and smooth for boundary nodes are achieved. An objective function method is proposed to locally optimize the degenerated quadrilaterals located on concave or large-curvature curves. In order to accommodate the need for overland simulations, the 1-D/2-D correspondence on river reaches, junctions with and without storage, ponds, lakes, dead ends and control structures is established. Finally, practical applications are provided to demonstrate the accuracy and reliability of the quadrilateral meshing algorithms proposed in this paper.     

基于三维多重网格法的抗滑稳定计算精度分析

在以有限元法来分析评价坝基、边坡的稳定安全度时,多重网格法将有限元分析网格和滑移块体的滑面网格作为独立的两套网格,滑面网格可随意切割有限元单元。这样一套有限元网格和一套应力成果就可以进行任意的滑块稳定分析。着重分析了多重网格法的精度。针对三维柱体和锦屏高边坡,研究两套网格如何匹配以提高计算精度进行处理,初步得出了一些有关多重网格法计算精度的知识。最后,应用基于多重网格法的第2类方法分析了锦屏左坝肩高边坡的稳定性问题。     

起伏地表下的复杂三维地质模型建立与重力异常计算

由于地质体和矿体的形态非常复杂，使用长方体网格离散建立正演模型时可能和真实情况有很大差别，因此计算结果可靠性差。本文提出一种基于约束Delaunay网格剖分的方法对地质体进行离散并进行重力建模，在模型边界等复杂区域使用网格自适应加密技术，将三维地质体离散为有限个四面体；并详细推导出针对四面体网格的重力正演公式，实现了基于约束Delaunay网格剖分技术的三维重力数值模拟；最后，针对一个合成数据模型，将计算解与解析解对比。结果表明，细化网格的模拟结果比粗糙网格更好，满足数值模拟的精度要求。将该方法应用到金川矿区实际地质体建模中，根据局部需要，建立各处网格密度不均匀的三维模型，并计算该模型的地表重力场，而后对比模拟数据与实测数据，结果表明Delaunay网格建模方法具有很强的适用性，能够模拟复杂的地质体重力异常。