数值计算

This thesis contributed to the comprehensive study of the Finite-Difference Time-Domain method and its application to the numerical computation of radiated electromagnetic fields in switched mode power supplies. The work includes mainly three parts: the study on the performance of PML absorbing boundary condition applied to pseudo low frequency electromagnetic problems; the validation of the FDTD method with PML absorbing boundary conditions and the corresponding computer software based on the numerical study of the electromagnetic field of an electric dipole antenna, and its application to the numerical computation of radiated electromagnetic fields in switched mode power supplies; the development of an improved alternating direction implicit finite-difference time-domain method.

在综合前人工作基础上，本文对时域有限差分法及其在开关电源辐射电磁场数值计算中的应用进行了系统的分析和研究，其核心内容包括：伪低频电磁场数值计算中PML吸收边界条件性能的研究；基于基准问题—电偶极子天线三维辐射电磁场，验证了本文构造的基于PML吸收边界条件的三维FDTD法及其计算软件，并应用于高频开关电源辐射电磁场的数值分析；提出了一种改进的交替方向隐格式时域有限差分法。

This paper used commerce software FLUENTS to implement numerical simulated compute because it could in more detail and comprehensive open out the distribution laws of the flow field in the channel and in the holes and the experimental results had been consummately enlarged. At last, the experimental results were contrasted and analyzed with the computational ones.

本文还利用商业软件FLUENT5进行了数值模拟计算，数值计算可以更详细更全面地展现通道内以及孔内流场的分布规律，更加丰富和完善了实验测量结果，并将实验结果和数值计算结果进行了对比分析。

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。

The author also writes a great amount of numeric computational sub-programs and programs too, almost include all respects of structural numeric computation using Daubechies wavelet. These programs not only test and verify the correlation results in this thesis, but also lay a strong foundation for expanding the application space of Daubechies wavelet in structural numeric computation.

本文还编制了大量的数值计算子程序和计算例程，几乎囊括了Daubechies小波有关结构工程数值计算的所有方面，这些程序的编制，不仅验证了本文的相关结论，同时，也为后续进一步拓展Daubechies小波在结构工程数值计算领域的应用空间打下坚实的基础。

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。

In this paper,a three dimensional elastic plastic hydrodynamical numerical method and the code MEPH3D using this method which can be used on high speed impact problems are introduced.

介绍一种可用于高速碰撞问题数值模拟的三维弹塑性流体动力学数值计算方法，以及应用该方法研制的应用软件MEPH3D，并给出了一些高速碰撞问题的数值计算结果，计算结果表明该程序具有计算三维高速碰撞问题的能力。

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。

It effectively solves the problem of contact mechanics between burden granules. The dynamic data structure that is a linked list is built to save and delete the varying data in simulation calculation process. Therefore, the distinct element method simulation model of charging bell-less top blast furnace is established in view of the distinct element method model of blast furnace burden granular.

本文首先对离散单元法的基本原理和数值计算方法进行了系统研究，针对高炉炉料颗粒介质特点，对离散单元法进行了相应改进，建立了高炉炉料颗粒运动的离散单元法基本数学模型，推导出了相应的高炉炉料颗粒离散单元法数值计算基本参数的计算公式，例如阻尼、刚度、时步等，并确定了合理的数值模拟参数值。

A three dimensional Navier Stokes equation is solved with a standard k ε turbulent model. Two experiments were carried out and the total pressure of jet flow was tested. Based on the tests, the differences between the calculated and test results were found to be 3% and 7% respectively. It proved that the results of calculation can well be used in engin...

研究采用数值计算和试验测量相结合的方法，控制方程为三维、雷诺平均 Navier- Stokes方程及 k-ε二方程的紊流模型，并且对该发动机进行了燃气流场的测试，对流场中的总压强进行了直接测量，进行了两次试验；在两次测点位置，试验结果与数值计算值相差分别为 3%和 7%；证明了对双喷管火箭燃气射流流场的数值计算具有了较好的精度，计算模拟结果可以用于工程设计中

The results of our numerical simulation show that the numerical method applied in our paper is practical, the calculation results match the actual situation properly; the digital images from numerical simulation possess a positive significance in understanding and improving the heat flow distribution of the meat dry kiln. The proposed method provides a feasible approach to analyze and improve the flow field of meat dry kiln with numerical simulation.

数值计算的结果表明：本文所用的数值计算方法是可行的，基本符合实际情况；所得计算结果分析图像对了解干燥窑中流场的分布情况和如何改善干燥窑流场分布具有积极的参考意义，本文所提出的方法为采用数值计算方法分析改善干燥窑流场问题提供了一种可行的手段。

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。