数值分析

The coordinate transformation and numerical integration was executed on the discretized tetrahedral elements based on which the 3-D MT vector-finite element method was implemented. A whole computation framework for 3-D vector-finite element method with unstructured mesh was given. Based on this some typical models were tested which has demonstrated that our algorithm could distinctively avoid problems caused by the fake solution and both the accuracy and efficiency were enhanced which made our algorithm has a bright future for further application.3. According to theory of Sobolev vector space and the discretization of Helmholtz space, the error estimate which was suitable for 3-D MT vector-finite element modeling was deduced by which the procedure of adaptive technique was guaranteed.4. Based on the fully unstructured tetrahedralization and optical strategy, the 3-D magnetotelluric h-adaptive vector-finite element method was presented through combining the error estimate. With this work, the accuracy and creditableness for 3-D MT complicatedly modeling was guaranteed.5. The 3-D magnetotelluric h-adaptive vector-finite element algorithm with unstructured mesh was implemented.

针对非结构化的四面体单元，采用坐标变换和数值积分方法，实现了MT三维矢量有限单元分析，建立起基于非结构化网格的三维MT矢量有限元计算流程，并对典型模型和国际标准电磁模型进行了数值模拟，结果对比和分析表明，基于非结构化网格的三维MT矢量有限元不仅消除了节点型有限元的伪解，而且具有很高的计算精度和速度，有广阔的应用前景。3、根据Sobolev函数的向量空间和Hemlholtz空间的分解，推导出基于残差的三维大地电磁矢量有限元后验误差估计公式，为三维大地电磁自适应矢量有限元数值模拟的实现奠定了基础。4、在完全非结构化四面体单元剖分及优化基础上，结合三维大地电磁矢量有限元后验误差估计公式，提出了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算策略，保证了对复杂大地电磁模型数值计算的精度和可靠性。5、实现了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算流程，对典型模型和国际标准电磁模型进行了数值模拟。

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。

This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.

本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。

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。

The geology research of carbonate reservoirs in Ordovician of Tahe oilfield showed that many large dissolved vugs and fractures were developed. The spread of the reservoir take on a very heterogeneous state. And the typical fractured-vuggy reservoirs was formed. According to the combination of the various spaces, the formation was divided into vuggy formation, fractured-vuggy formation and fractured formation. The research showed that development of the vug is relevant to the its position on the structure, the fractures, the water surface and the weathering surface. Multi-phase charge and recharge of the oil in the reservoirs resulted in the complexity of the fluid distribution. So the"Bottle Model"was brought forward to explain the movement of the water-oil contact. The special storage space and the complex fluid distribution lead to the unstability of the production and the complexity of the water cut. In order to explain the characteristic of the fracture-vug unit was brought forward and the basic principle and method of the partition of the fracture-vug unit was formed. The classification and evaluation of the units were performed according the reserve and energy. Based on the research of geology characteristic and the fluid flow in the reservoir the comprehensive numerical simulation plan of the fractured-vuggy reservoirs were established. Through the selection of the simulation unit, fluid flow type and parameter equivalent the triple media reservoir simulation model was established. Considering the practical application the model was resolved by the DKR decomposition conjugate grads method. Based on the fine reservoir description of Dsitrict IV of the Tahe oilfield the various space type were classified and combined together. The geology model of Unit S48 was constructed. Two typical single well model was established according to the geology and the dynamic phenomena. Finally the single well model and the Unit S48 were simulated by the triple media reservoir simulator. Via the local grid refinement and coarsening in the simulation good matchs were gained. Based on the results of the simulation the reserve distribution, percent of reserve produced in various space and the natural energy were analyzed. The fluid was storaged in the fractures and vugs mostly and more than 90% the produced oil came from the systems. The energy belonged to the active one. The results of simulation accorded with the fact and showed the validity and practicability the research and the simulator.

塔河油田奥陶系碳酸盐岩油藏的地质研究表明，其储层中发育着很多大型的溶蚀洞、缝，储层的平面展布呈现出极度的非均质性，形成了典型的缝洞型碳酸盐岩油藏，根据各种孔隙介质在储层中的组合，将储层分为了溶洞型、裂缝-溶洞型和裂缝型三类；研究表明溶洞储层的发育和构造位置、裂缝的发育、潜水面和风化面的位置等因素有关；多期充注的油气成藏模式导致了流体复杂的赋存状态，由此提出了所谓的"瓶子模型"，解释生产过程中油水界面的变化；特殊的储集空间类型和流体分布特征导致油田在开发过程中表现出很大的不确定性和含水变化的复杂性，为了合理的解释油气田开发过程中的动态特征，提出了"缝洞单元"的概念，并制定了"缝洞单元"纵横向划分的基本原则和依据及划分方法，并对"缝洞单元"进行了分类和评价；基于地质特征和流体在其中流动规律的研究，提出了缝洞型碳酸盐岩油藏的数值模拟综合解决方案，通过模拟单元的选择、流动类型和参数的等效，建立了三重介质油藏三维三相数值模拟模型，采用不完全LU分解预处理共轭梯度法进行了求解；在塔河油田4区精细油藏描述的基础上，将各种类型的孔隙空间进行了归类组合，建立了S48单元的地质模型；通过对油井生产动态进行分析研究，建立了两类和油井地质、生产动态相对应的单井模型；最后应用三重介质油藏数值模拟软件对单井模型和S48单元进行了数值模拟，通过局部加密和粗化等技术模拟流体流动规律，取得了很好的拟合效果；结合数值模拟结果，分析了各种介质中的储量分布、储量产出的百分比以及地层的能量，认为塔河油田缝洞型油藏中流体绝大多数储集于缝洞系统之中，所产出流体90%以上也来自于缝洞系统，其底水能量属于较充足的类型；模拟结果和油田实际情况符合较好，说明了地质研究和油藏数值模拟研究的正确性。

The geology research of carbonate reservoirs in Ordovician of Tahe oilfield showed that many large dissolved vugs and fractures were developed. The spread of the reservoir take on a very heterogeneous state. And the typical fractured-vuggy reservoirs was formed. According to the combination of the various spaces, the formation was divided into vuggy formation, fractured-vuggy formation and fractured formation. The research showed that development of the vug is relevant to the its position on the structure, the fractures, the water surface and the weathering surface. Multi-phase charge and recharge of the oil in the reservoirs resulted in the complexity of the fluid distribution. So the"Bottle Model"was brought forward to explain the movement of the water-oil contact. The special storage space and the complex fluid distribution lead to the unstability of the production and the complexity of the water cut. In order to explain the characteristic of the fracture-vug unit was brought forward and the basic principle and method of the partition of the fracture-vug unit was formed. The classification and evaluation of the units were performed according the reserve and energy. Based on the research of geology characteristic and the fluid flow in the reservoir the comprehensive numerical simulation plan of the fractured-vuggy reservoirs were established. Through the selection of the simulation unit, fluid flow type and parameter equivalent the triple media reservoir simulation model was established. Considering the practical application the model was resolved by the DKR decomposition conjugate grads method. Based on the fine reservoir description of Dsitrict IV of the Tahe oilfield the various space type were classified and combined together. The geology model of Unit S48 was constructed. Two typical single well model was established according to the geology and the dynamic phenomena. Finally the single well model and the Unit S48 were simulated by the triple media reservoir simulator. Via the local grid refinement and coarsening in the simulation good matchs were gained. Based on the results of the simulation the reserve distribution, percent of reserve produced in various space and the natural energy were analyzed. The fluid was storaged in the fractures and vugs mostly and more than 90% the produced oil came from the systems. The energy belonged to the active one. The results of simulation accorded with the fact and showed the validity and practicability the research and the simulator.

塔河油田奥陶系碳酸盐岩油藏的地质研究表明，其储层中发育着很多大型的溶蚀洞、缝，储层的平面展布呈现出极度的非均质性，形成了典型的缝洞型碳酸盐岩油藏，根据各种孔隙介质在储层中的组合，将储层分为了溶洞型、裂缝-溶洞型和裂缝型三类；研究表明溶洞储层的发育和构造位置、裂缝的发育、潜水面和风化面的位置等因素有关；多期充注的油气成藏模式导致了流体复杂的赋存状态，由此提出了所谓的&瓶子模型&，解释生产过程中油水界面的变化；特殊的储集空间类型和流体分布特征导致油田在开发过程中表现出很大的不确定性和含水变化的复杂性，为了合理的解释油气田开发过程中的动态特征，提出了&缝洞单元&的概念，并制定了&缝洞单元&纵横向划分的基本原则和依据及划分方法，并对&缝洞单元&进行了分类和评价；基于地质特征和流体在其中流动规律的研究，提出了缝洞型碳酸盐岩油藏的数值模拟综合解决方案，通过模拟单元的选择、流动类型和参数的等效，建立了三重介质油藏三维三相数值模拟模型，采用不完全LU分解预处理共轭梯度法进行了求解；在塔河油田4区精细油藏描述的基础上，将各种类型的孔隙空间进行了归类组合，建立了S48单元的地质模型；通过对油井生产动态进行分析研究，建立了两类和油井地质、生产动态相对应的单井模型；最后应用三重介质油藏数值模拟软件对单井模型和S48单元进行了数值模拟，通过局部加密和粗化等技术模拟流体流动规律，取得了很好的拟合效果；结合数值模拟结果，分析了各种介质中的储量分布、储量产出的百分比以及地层的能量，认为塔河油田缝洞型油藏中流体绝大多数储集于缝洞系统之中，所产出流体90%以上也来自于缝洞系统，其底水能量属于较充足的类型；模拟结果和油田实际情况符合较好，说明了地质研究和油藏数值模拟研究的正确性。

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。

This is the University analysis of the experiment- Romberg algorithm source code, to help you learn and master the Romberg al...

· 这是大学数值分析的实验——龙贝格算法的源码，帮助大家学习和掌握龙贝格算法！

Also we discuss the classic model--- Peirce's plain stitch model, pointout an error in it, and give some useful parameters.

我们对经典的 Peirce 模型进行了讨论，并进行了数值分析，指出了模型中存在的问题，并给出了常用的参数。

The MHD stirring chamber has found it's application in micro c...

建立了搅拌混合器的理论模型，并对其动力特性进行了数值分析，理论结果与实验结果相吻合。

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。