数值方程

The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. The advantage is that the cost function variation is independent of the flow field variation, with the result that the gradient of cost function with respect to arbitrary number of design variables can be determined without the need for additional flow-field evaluations. So each design cycle requires the numerical solution of both the flow and the adjoint equations leading to a computational cost roughly equal to the cost of two flow solutions.

虽然他们的研究成果大多数都可以在公开性文献上看到，但是其中一些具体的细节问题的处理方法却没有透露，比如：伴随方程如何离散求解才能减小最终梯度计算中的误差，使得设计过程有效地进行；伴随方程与流动方程的边界条件是不同的，如何合理地处理伴随方程的边界条件，才能推动设计过程朝着设计目标而发展；在减阻问题中目标函数如何定义，求解梯度的具体数学公式如何推导，如何通过数值方法来实现它们等。

The coefficients in trial function can be gained by the point collocation method, then the solution of the boundary value problems is obtained. Non - uniform beams and irregular plates on Winkler foundation and plates on elastic half space foundation can be numerical calculated by the introduced method.

为对土与结构物的相互作用进行研究，在采用适当的土体模型的基础上，必需求解地基与基础的共同作用方程，而该共同作用方程一般是偏微分方程或微分积分方程，除一些简单的模型外，其解析解较难获得，因此只能采用数值方法求其结果，加权残仇法是一种L作鼠少、简便易行的数仇方法{2，但其解的精度'。

Experimental results show the recognition rate of the method is 95%for a known expresser and 72% for a novel expresser. Aiming at the shortcomings of optical flow technique,two improved optical flow algorithms are presented.One way is to introduce forward and backword constraint eqution and Hessian matrix of optical flow equation is computed.The well- posedness of each point of local neighbourhood is examined and the weight of Lucas-Kanade's method is defined as the reciprocal of the conditioning number of its Hessian Matrix.

3针对传统光流法的缺点，分别提出了两种不同的改进方法：其一为引入前向-后向光流方程，计算其Hessian矩阵，把Hessian矩阵条件数的倒数作为Lucas-Kanade光流法的加权阵，可有效消除局部邻域中不可靠约束点，同时提高基本约束方程解的稳定性；其二为针对传统光流法只适用于刚体运动的特点，在扩展约束光流方程的基础上引入了div-curl样条函数作为扩展光流约束方程的附加约束条件，给出了一阶和二阶div-curl样条约束下光流的数值解。

In this article, with pointing out that the result of the current calculation model is deficient in the similarity, it has deduced the numerical regulation of the variation of the elements including q ,γ andτ in the steam-water distribution matrix equation when the terminal temperature difference exits in the heater via the power balance equation, and combining with the power equation and boiler absorbed heat equation, the precise calculation model for the impact of heater terminal temperature difference on heat economy of unit is then derived.

指出现有计算模型结果具有近似性的不足，本文通过加热器能量平衡方程推导出加热器有端差时汽水分布方程中q 、γ和τ元素数值的变化规律，然后结合功率方程和吸热量方程得到加热器端差对机组热经济性影响的精确计算模型。

Based on Crank-Nicoson's technique, and a new approach for the numerical simulation of the model is raised. The truncation error of the one step difference method reaches O (△t^2+△x^2) and of quite good stability condition.

基于Coriolis加速度和Lagrangian应力公式，利用Newton第二定律导出轴向加速度运动弦线横向振动的动力学模型；通过线性变换将方程化为一阶无量纲的非线性微分方程组；并利用Crank-Nicoson的中点离散技巧，给出运动方程的单步二阶差分方法；算法把对运动方程和本构方程分别离散，使之可以用于不同本构的运动弦线的数值仿真。

Then, under the consideration of mixed boundary value condition, a pair of dual integral equations for the rocking vibrations of a disk on saturated grounds are obtained, which can be reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Consequently, the dynamic compliance coefficient is evaluated and numerical results are presented to portray the influence of poroelastic effects on the dynamic interaction problem.

对于刚性圆板，作者首先采用Hankel变换对波动方程进行求解，得到了该控制方程在Hankel变换域内的通解，然后由混合边值条件建立了饱和地基上刚性基础摇摆振动的对偶积分方程，并将其化为第二类Fredholm积分方程，用数值方法计算了不同频率下基础的动力柔度系数，从而考察孔隙水的存在对基础摇摆振动特性的影响。

The process of shock mechanical energy flowing into the molecule of the en-ergetic material is expounded.According to the hyperbolic type thermal conduc-tion equation,the author modifies the mathematic model describing intramolecu-lar vibrational state pumping,which was presented by D.D.

论述了冲击机械能向含能材料分子内部流动的过程，结合双曲型的热传导方程修正了国外一些学者提出的分子内部振动态泵浦的数学模型，提出了一组与他们的方程不同的非线性偏微分方程，根据方程的试探解，用迭代方法，得到了数值解。

The powerful function of a new computer language MATLAB, produced by the America Mathworks company, is the mathematical software system for the calculation in science engineering. It can efficiently solve problems in science and engineering such as numerical linear hypercomplex system, digital approximation, optimization, numerical quadrature etc. It also has characters of beautiful interface and convenience for users.

MATLAB是Mathworks公司推出的适用於科学和工程计算的数学软件系统，可高效地解决数值线性代数、微分方程数值解、数值逼近、最优化、数值积分等科学和工程问题，且具有可视化图形处理、使用方便、开放式多功能於一体的新一代计算机语言。

Chapter 4 of this dissertation has carried out a physical simulation study about the processes of formation and laws of evolution of the fan delta in Baimiao gas field. Based on the results of the study about the geological background in this area, this paper has discussed about the sedimentation facies marks for the fan delta in Baimiao gas field, worked out a detailed proposal about the development of physical simulation experiment about the fan delta, and described in detail the general laws and major controlling factors governing the sedimentation processes of the fan delta. A detailed measurement was made about the experimental results, and a systematic comparison was made relative to the prototypic characteristics. Based on the observation and description about the experimental processes and the analyses about the experimental results, this paper has give

在本章中，指出了数值模拟研究的基本特点，给出了扇三角洲形成过程的基本控制方程和数学解法：在此基础上设计和开发了扇三角洲形回成过程的平面二维数值模拟软件，并对计算过程中所遇到的主要问题一计算速度较慢开展研究，对比了以天、旬、月为时间单元进行汁算对沉积结果的影响，研究认为，在流量无突变的情况下，可以适当增长计算的时间步长和适当放松精度要求；根据白庙气田扇三角洲的基本地质特征设计了数值模拟计算的基本条件，以月为单位，计算了扇三角洲四百年的形成过程及演化规律，并以50年为单位输出沉积结果；本章最后还对数值模拟方法及结果进行了讨论。

A numerical solution of the isothermal EHL problem for finite line contacts has been pressnted which is convergence in moderate load and material parameters.

二。用差分格式离散二维Reynolds方程，通过间接求解的方法，推出了中等载荷和材料参数下收敛的等温有限长线接触弹流数值计算方法，有效地克服了等温有限长线接触Reynolds方程的强各向异性所产生的数值计算易发散问题。

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。