数值方法

Numerical differentiation is that derivative value of a function at a certain point is approximately solved in discrete method.

中文摘要：数值微分就是用离散方法近似地求出函数在某点的导数值，关于数值微分已有许多求解方法，但这些方法都有各自的局限性，并且关于高阶导数近似逼近的方法研究相对较少。

The main objective of this dissertation was to develop methodologies with capability of engineering application for simulating flow in fractured rock using discontinuum models. The study work includes three parts. In the first part, numerical methodology of three-dimensional discrete fracture network model casing on hybrid BEM-channel was presented, and the technique for improve the model's computing efficiency was also studied. Firstly in this part, computer simulation methodology based on the Baechermodel for generating network of discrete fractures was presented, which includes the follow details: probability distributions of fracture density,orientation, trace length, size, and aperture and estimation of their statistical parameters; stochastic models of fracture network; Monte-Carlo's simulation method; numerical simulation procedure and technicality.

给出了离散裂隙网络模型所依据的基本假定；发展了基于Baecher模型的离散裂隙网络计算机随机生成技术：详细地推导了单裂隙渗流和多裂隙相交网络渗流的边界单元法公式，发展了离散裂隙网络中稳态渗流的边界元数值技术，并且讨论了相关的具体数值技术细节，如角点的处理方法，单元的自动剖分等：描述了混合边界元—管流模拟方法及其数值实现；研究了裂隙网络的简化方法，并针对裂隙网络边界元法的特点提出了一种改进的分块三角分解法。

With the investigation of the domestic and foreign literature systematically, the bases on the domestic and foreign present research and the comprehensive utilizations of the various knowledge of fluid mechanics in porous medium, reservoir engineering, mathematical physics, perforation completion, numerical simulation and so on, this article takes numerical simulation of gas reservoir of water solubility as the research aim which has completed following research works and obtained the corresponding research results: it analyzes the nature of the Water-soluble gas and formation water as well as the influent factors of the solubility through the study of massive materials; It establishes mathematical models three-dimension, the dual medium, the gas-water phase through the way of finite difference in the migration of water-soluble gas, which describes the entire process of release, migration and production in formation, where it considered the problems of variable bubble point; According to the numerical models of gas reservoir of water solubility it provides solution procedure that based on black oil model; It discovers that there will obtain the good effects in the lowly speed of development through simulation; the reinjection of formation water may largely enhance the produce degree of water-soluble gas when we consider reinjection in simulator; It considered the influence of perforated completion on development so as to increase the simulator"s versatility, It discovers that the simulator may reflect the conditions of development when we exanimate he simulator"s reliability with the empirical datum.

本文以水溶性气藏数值模拟研究为研究目标，在系统调研国内外文献、深入分析国内外研究现状的基础上，综合利用渗流力学、油气藏工程、数学物理方法、射孔完井以及数值模拟理论等多方面的知识，完成了以下研究工作并取得相应的研究成果；①通过对大量的资料调研，分析了水溶气、地层水性质、储层地质性质以及影响气体在水中溶解度的因素。②考虑到由于高压产生的大量水力裂缝，采用有限差分方法建立水溶气运移的三维、双重介质、气-水两相全隐式数学模型，该模型描述了水溶气在地层中的释放、运移和采出的整个过程。③在原有黑油模型的基础上，根据水溶性气藏数值模型编制了该数值模型的求解程序，该程序可以求解单重、双重介质两种情况。④通过模拟不同开采速度对水溶气开发效果的影响，发现开采速度较慢的时候可以取得较好的开采效果。⑤在模拟器中考虑了注水对水溶性气藏开发的影响，地层水回注可以大幅度提高水溶气的采出程度。⑥为增加模拟器的通用性，在模拟器中考虑了射孔完井方式对开采的影响。⑦检验模拟器计算的可靠性，发现在使用实验数据对水溶性气藏进行模拟时，模拟器可以很好的反映气藏开发的状态。

The mechanical behavior of Shape Memory Alloys material is tested, and the constitutive model of the SMA is established. A kind of SMA combined rubber isolator is developed, and the isolation effect of the SMA combined rubber isolator for long-span bridge and tall building structures is numerically simulated, from which the adaptive isolation performance and the self-restoring capacity of the SMA combined rubber isolator are verified. A kind of SMA damper is developed, the mechanical behavior of the SMA damper is tested, and the model of restoring force of the SMA damper is established. The theory and method of adaptive control based on the SMA damper for the long-span bridge are built, and the effectiveness and reliability of the adaptive control for the long-span bridge using the SMA damper are verified through numerical simulation and model test. The MRF-04K type magnetorheological damper is developed, the mechanical behavior of the MR damper is tested, and the model of restoring force of the MR damper is established. The theory and method of adaptive control based on the MR damper for the long-span bridge and tall building structures are built, and the effectiveness and reliability of the adaptive control for the long-span bridge and tall building structures using the MR damper are verified through numerical simulation and model test. In addition, the theory and method of sub-structural damage identification for long-span bridge are derived, the influence of soil-structure dynamic interaction on the seismic isolation and control effects with different isolation and control measures and the damage responses and the sliding base-isolation of large structures under the excitation of underground explosion are investigated.

试验研究了形状记忆合金材料的力学性能，建立了SMA材料的本构模型；研制了一种SMA复合橡胶隔震支座，数值仿真分析了应用SMA复合橡胶支座的大跨桥梁和高层建筑结构的隔震效果，从而验证了SMA复合橡胶支座的自适应隔震性能及其震后自恢复能力；研制了一种SMA阻尼器，试验研究了SMA阻尼器的力学性能，建立了SMA阻尼器的恢复力模型，建立了基于SMA阻尼器的大跨桥梁结构自适应控制理论与方法，通过数值仿真与模型试验验证了大跨桥梁结构SMA阻尼器自适应控制的有效性与可靠性；研制了一种MRF-04K型磁流变阻尼器，试验研究了MR阻尼器的力学性能，建立了MR阻尼器的恢复力模型，建立了基于MR阻尼器的大跨桥梁和高层建筑结构的自适应控制理论与方法，通过数值仿真和模型试验验证了大跨桥梁和高层建筑结构MR阻尼器自适应控制的有效性与可靠性；还建立了大跨桥梁结构的子结构损伤识别的理论与方法，研究了土-结构动力相互作用对不同隔震和控制措施的减震控制效果的影响以及地下爆炸波作用下各类大型结构的灾害响应与滑移隔震。

Recent years as development of the computer and software, it becomes reality using numeric simulation to research grouting in clay. Using the software of PFC2D, the grouting in clay is lucubrated and such achievements are reached: Grouting technologies in existence grouting material and serosity are studied and rational methods are put forward in choosing grouting technology and serosity.(2) Base on numeric simulation biax test a method is explored to simulate clay with PFC2D.(3) A method is explored to simulate grouting using PFC2D.(4) The relation between serosity pressure and diffuseness of grouting in clay with different initial stress is studied.(5) The stress transformation of clay is studied during grouting.(6) The stress distribution is studied under different serosity pressure.(7) The normal stresss and shear stresss at any section are studied.

近年来随着计算技术的发展，使得采用数值模拟的方式研究均质土体中的注浆成为可能，本文则利用离散元程序PFC2D对均质土体中注浆进行了研究，主要做了以下几方面的工作：(1)研究了现有注浆加固技术、注浆材料以及浆液的性质，阐述了合理选择注浆方式以及浆液的方法；(2)采用数值双轴实验，探索了应用离散元模型模拟土体的方法：(3)探索了采用颗粒流程序进行注浆数值模拟的方法途径；(4)研究了在粘土中注浆不同侧向土压力条件下浆液扩散范围与注浆压力规律；(5)研究了注浆过程中不同阶段土体中压应力的变化；(6)研究了不同注浆压力对土体应力分稚的影响：(7)研究了注浆过程中土体中任一截面处正应力与剪应力的对比关系。

The new singular element at the end of a blunt crack is obtained,the new method for calculating stress intensity factors of blunt crack problems is presented.

利用其局部解构造了一种新的大曲率缺口位移模式；建立含大曲率缺口损伤结构有限元方程和与相应的缺口奇异单元；提出了求解大曲率缺口应力与应力强度因子等断裂参量的数值计算方法，数值算例说明本文方法是一种有效的数值计算分析方法。

In this thesis, I summarize the theoretical calculation method, applied scope and notice of siphonic drainage system, and point out the advantage of siphonic drainage system compared with gravitation drainage system. In the archetype experiment study of siphonic drainage tube, I adopt different tube diameter and different structural height to survey the drainage volume and press in different place. I observe various kinds of flow state, and get chief factors which influence hydraulic peculiarity of system as the tube diameter or structural height, and find out the relevance of factor to flux. I apply CFD Fluent software and adopt standard k-ε model and RNG k-ε model, then use finite volume method and second-order upwind scheme to discrete numerical model, while coupling numeration of velocity field and press is based on SIMPLE. In the numerical simulation of curved part of tube, siphonic drainage tube experiment system and multi-outlet siphonic drainage system, I make research on internal velocity and press of system in different project condition by changing the tube diameter of curved part, negative press value in tube export and improving the quantity of water gutter. This thesis first adopts a method of combining archetype experiment and numerical simulation to study the siphonic drainage system, test and verify the validity of experiment and numerical simulation, and makefurther study on system, it solves the problems of limited testing conditions, and has a logical results, it can provide a valid method for optimizing and designing the drainage tube-net system. The conclusion have referring value for study and design of siphonic drainage system.

本文首先对虹吸式排水系统理论计算方法、适用范围以及注意事项做出总结，并分析了虹吸式排水系统的优势；再对虹吸式排水管道进行原型试验研究，采用不同管径不同立管高度，对系统流量、管道压强进行量测，观察了各种工况下的流态，对其水力特性进行研究分析，找出影响水力特性的落差、管径主要因素以及与排水量的关系；进一步应用计算流体力学Fluent软件，采用标准κ-ε模型与RNGκ-ε模型，计算过程应用有限体积法和二阶迎风格式对数值模型进行离散，速度和压力的耦合采用SIMPLE算法，分别对系统弯管段、虹吸排水管道试验系统、多斗虹吸式排水系统进行数值模拟分析，通过改变管段弯头处半径、管段出口负压值、增加雨水斗数对不同工况下系统内部的速度和压力进行研究；本文首次采用结合原型试验与数值模拟相结合的方法，对虹吸式屋面雨水排水系统进行研究，试验与模拟相互验证，并进行拓展，很好地解决了虹吸式屋面雨水排水系统由于试验条件限制问题，结果正确合理，为排水管网系统设计和优化研究提供了有效的方法，对工程设计有较好的参考价值。

We take the nonlinear Klein-Gordonequation in an infinite strap and in a cylinder as examples to illustrate how to deal withnonlinear problems by using Jacobi pseudospectral methods.

Jacobi谱方法和拟谱方法数值分析理论的研究极大地丰富了现有谱方法的理论基础，同时将发展泛函分析、数值逼近论和偏微分方程数值解的相关理论。

Based on them, distribution laws of subgrade temperature field under fluctuant boundary temperature cycle conditions are analyzed, and different ratios of slope for general subgrade and different status when there are or not banquettes are compared by laboratory simulation and numerical analysis; thermal insulation and cooling effect of thermal insulation slab, broken stone and non-power heat pipes is respectively investigated under the trend of elevated temperature by numerical analysis, laws of subgrade deformation are predicted under the trend of elevated temperature and influences of subgrade thaw settlement on pavement stress are studies by numerical computation for observation data of representative road sections selected.

为研究青藏公路冻土病害处治对策，从青藏公路2002年～2004年冻土病害整治工程实际出发，在系统分析研究青藏公路病害及发生机理的基础上，运用室内模拟试验、数值分析方法，依托处治冻土病害路段实际使用的隔热板路基、碎石路基、无动力热棒路基等进行现场试验，分析边界温度周期波动条件下的路基温度场分布规律，同时进行一般路基不同边坡坡率的对比研究及有无护坡道的对比研究；运用数值分析方法，对气温升高趋势下隔热板、碎石、无动力热棒的隔热降温效果进行了研究；选择代表性路段观测资料，运用数值计算的方法，进行升温趋势下的路基变形预测，研究路基融沉变形对路面应力的影响。

In the second part of the paper, the sport techniques of the flight elements was analysised in-depth theoretically by the movement technical structure:①the giant swing was first analysised in mechanics by applying the Kane's method, the dynamic equation of 5-link multi-body model was established, and the computer simulation software of the giant swing on the high bar was developed.

其次，作为单杠上飞行动作系统性研究的另一主要方面，本论文对飞行动作一般技术结构中的各技术环节进行了深入的理论分析：①着重对飞行动作准备阶段的回环运动技术进行了动力学分析，主要采用了多体力学理论中的Kane方法，建立了5环节人体回环运动的动力学方程，并应用计算机数值仿真技术研制开发了用于回环运动动力学分析的数值仿真软件，进而以动作实例对回环运动进行了数值仿真与误差分析，其所得到的数值仿真结果能够满足对人体回环运动的动力学分析和仿真要求；②对于飞行动作的撒手技术环节，本论文从人体环节相对运动角度，来分析撒手时人体质心的运动以及撒手时角动量参数，并列举了几种飞行动作撒手技术的基本力学指标；③关于飞行动作的空中技术，论文在总结了空翻转体动力学机理的研究成果基础上，对人体空中运动定量化问题进行了一般性描述，并进一步应用刚体动力学理论，着重建立起了描述空翻与转体技术之间定量化的关系，讨论了空翻转体运动的稳定性及其运动模式的转换问题，它对于定量地评定空翻转体技术以及今后对空翻转体动作进行数值仿真都具有理论上和实践上的重要意义；④关于飞行动作再握技术环节，本论文避免了以再握瞬时性的力学参数指标来描述再握技术特征的简单化途径，提出以再握下摆与回环下摆相对比的方法来研究再握技术，并以飞行动作再握技术的具体实例进行了对比分析，表明再握下摆技术相比回环下摆技术有着相当的困难性和复杂性，运动员对再握下摆过程中各环节的相对运动实施有效的控制，是连接高难动作以及顺利流畅地完成成套动作的关键。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。