数值

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。

The computing plots of the solutions from the two methods were inconsistent under the specified boundary-initial conditions, which stirred up the debate of the effectiveness of Maxwell's equations in lossy medium. It is found that the differences between the two numerical curves can be viewed as the Gibbs phenomenon caused by cutting off the high frequency components in computing the infinite integral of the numerical curve of Harmuth's solution.

通过比较两种解析解的数值曲线得出：两者的差异在于求解Harmuth解的数值曲线时，采取无穷积分的高频截断近似产生了吉布斯现象；在计算Harmuth解的数值曲线时不断增大积分上限，其数值曲线的振荡不断向不连续点处收缩，而且衰减加快，因此在求解Harmuth解的数值曲线时，若积分区间取为理想无限大，则可以预见相同计算精度下两种方法的电场解的数值曲线是一致的。

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

本研究在探讨数值积分程式之平行化，所使用的演算法为林聪悟与林佳慧[1997]一书所提出的「Romberg树自动布点数值积分」架构，此一数值积分方法能以适应被积函数值变化情形方式自动安排积分点来进行数值求积计算，在提高阶数以获得更高精度积分值的过程中，此一方法只须再计算新增加积分点的函数值，搭配先前已计算过的函数值的重覆运用即可获得更精确的数值积分估计值，如此将能减少升阶过程中函数求值计算的次数，有效率地完成单重积分的数值计算。

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。

Numerical Analysis - Dave Rusin; The Mathematical Atlas 数值分析----Dave

本页为短篇论文的集合，用来提供一个对数值分析的介绍。

Numerical Analysis - Dave Rusin; The Mathematical Atlas -数值分析----Dave Rusin

数学文集。本页为短篇论文的集合，用来提供一个对数值分析的介绍。

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 method of CFD numerical simulation is employed to replace experimental investigation. Hence, STAR-CD of the commercial software is used to simulate the outer flow field and heat transfer performance of integrated heat sink with heat pipes cooled by airflow. It is found that simulated results agree with experimental results well, which indicates that simulation method is reasonable and reliable. Further, simulated computations for different fin thickness, fin pitches and air velocities are performed to analyze their effects on heat transfer performance of heat sink. Finally, a new optimized structure of integrated heat sink with heat pipes is provided to meet future demands for cooling CPU and its heat transfer is also evaluated. For multi-heat source and higher dissipation power of electronic devices, the integrated heat sink with heat pipes attatched fins stagged in different positions of channels is presented and its flow and temperature fields are also simulated to enhance heat transfer. As a conclusion, all mentioned above are useful for the design of heat sink with excellent efficiency of heat dissipation and further research.

应用商业软件Star-CD对CPU集成热管散热器的外部流场和传热特性进行了数值模拟，将数值模拟结果和试验结果对比，验证了所提出的数值计算方法是可靠和可行的；利用此数值模拟方法对CPU集成热管散热器在不同散热翅片间距、厚度和气流速度下散热器的流动与传热性能进行了数值计算，分析了这些参数的变化对散热器传热性能的影响；针对未来CPU冷却的要求，确定了与最优气体流速匹配的最佳翅片间距、厚度的CPU集成热管散热器的新结构；利用试验评测了根据数值模拟提供的新结构开发出的新CPU集成热管散热器的传热性能；最后在场协同强化传热的理论的基础上，对CPU集成热管散热器的散热翅片错位排列来强化散热器的散热，满足未来大功率、多热源的电子元件的散热，为今后进一步优化散热器提供了依据。

Main research works are as follows:(1) Numerical simulation of turbulent flow and combustion in power plant furnace (2) Numerical simulation of fire spread and crown fire in forest fire behave (3) Numerical simulation of burning process of large space building (4) Numerical simulation of three-dimensional fluid flow of satellite cabin in microgravity environment (5) Numerical simulation of burning process of multi-rooms It shows that the ability of FAC3 and FZ code is strong and the code is widely used for practical problems.

研究工作主要涉及以下几个方面：（1）电站煤粉锅炉流场的数值分析（2）林火行为中火蔓延和树冠火等特性的数值研究（3）大空间建筑火灾烟气流动过程的数值分析（4）微重力条件下卫星密封舱内部流场的数值分析（5）多室火灾过程的数值分析研究工作表明，FAC3和FZ程序的功能较强，通用性较好，可对多种热过程现象进行数值模拟，在一定程度上讲，即可用于科学研究，又可用于实际工程问题，并具有广泛的应用前景和推广价值。

Professor L N Trefethen, Numerical Analysis - Balliol College, Oxford University, UK - L N Trefethen教授,数值分析----牛津大学Balliol

学院。链接到牛津大学数值分析研究团体出版的图书与近期发表的论文。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。