数值分析

As important ways for numerical solutions of partial differential equations, spectral methods have been developed rapidly in the past several decades. They not only have been widely applied to numerical simulations in various fields such as physics, mechanics, aerology, oceanics etc, and their theories of numerical analysis also tend to perfect.

作为数值求解的一种手段，谱方法在近几十年得到了蓬勃的发展，它不仅被广泛运用于物理、力学、大气、海洋等领域的数值计算，而且它的数值分析理论也不断地趋于完善。

Finite difference method is adopted in this model to analyze the temperature distribution and fulgurite resistance of a fuse.

针对所提出的简化模型，用直接差分法进行数值模拟，设计出用直接差分法进行数值计算的通用程序，实现了温度分布和弧后残躯电阻的数值分析。

Impsons Integration: In numerical analysis, Simpson s rule is a method for numerical integration, the numerical approximation of definite integrals.

pecifically：：辛普森整合：数值分析中，辛普森法则是一种方法，数值积分，数值逼近定积分。具体来说

By the numerical analysis of the ultimate bearing capacity of two- and three-dimensional footing under combined loading mode, the results show that the effect of alteration of underground water lever on bearing capacity of three-dimensional foundation is more than on that of two-dimensional foundation, the effect of soil gravity on bearing capacity of three-dimensional foundation is more than that of two-dimensional foundation. At the same time, the numerical calculation process of ABAQUS indicates that whether the geostatic stress is balanced or not has great effect on the numerical convergence. In view of the effect extent of dilation angle of soil on the ultimate bearing capacity and the failure pattern of foundation, the condition of two-dimensional plane strain is higher than that of the three-dimensional foundation.

复合加载模式下，通过对三维矩形基础和二维条形基础进行数值分析，结果表明：黏性土地基中地下水位的变化，对三维矩形基础极限承载力的影响程度高于对二维条形基础的影响；在求解地基极限承载力的过程中，土体重度对三维矩形基础的影响明显高于对二维条形基础的影响，同时ABAQUS数值计算过程表明，地基土体地应力能否合理平衡，对数值求解过程中是否收敛有很大的影响；就土体剪胀角对地基极限承载力的影响程度而言，二维平面应变情况下土体剪胀角对极限承载力的影响比三维情况下的影响更明显，即土体剪胀角对条形基础极限承载力的影响高于三维矩形基础。

It is not enough to resolve all of the problems related to the hydraulic stability only to analyze the stable field in passing components. Finally, the paper numerically simulated the transient field in prototype's draft tube under different operating conditions by means of Reynolds stress turbulence model and analyzed the law of motion of vortex rope as well as the performance of low-frequency pressure pulsation and compared with field test results.

仅仅对机组的过流部件进行稳定场的CFD数值分析还不足以解决所有与水轮机水力稳定性有关的问题，因此在本论文的最后，采用雷诺应力湍流模型对真机尾水管在不同运行工况下进行了非稳定场的CFD数值解析，分析涡带的运动规律及其产生的低频压力脉动特性，并与真机的试验结果进行了比较，结果比较吻合。

Based on the results from the Kaiser effect test, disengagement density dislocation test calcspar mineral crystal lattice, and physical simulation results, the numerical simulation models are constructed, and the boundary conditions for simulation analysis is decided.

利用Kaiser效应、方解石矿物晶体的晶格自由密度位错的测试结果，结合物理模拟的结果，建立了研究区数值模拟分析的地质模型，确定了数值分析的边界条件。

Because the techniques of the biochemical waste treatment are very important, the techniques of the cultivation of the microorganism have received more attention in recent years. A study is conducted to analyze the steady states and dynamic bechavior of the reactions of the cell-substrate and the prey-predator interaction in two chemostats in series. For the reaction of cell-substrate in two chemostats in series, if the specific growth rate of the Monod model is used for the cell , there are three types of steady states for this reaction system. These three types of steady states and stability are analyzed in detail. The dynamic behavior of this reaction system is analyzed by the numerical method and computer graphs. The results show that the dynamic behavior of this system consists of stable steady states.

由於生物废弃物的处理技术相当重要，故最近几年来微生物的混合培养技术深受大家的重视，本研究实施菌类－基质(Cell-Substrate)和被捕食者－捕食者(Prey-Predator)相互作用之生化反应在两个生化反应槽串联之稳定状态和动态分析，对於菌类－基质之生化反应，若以Monod模式来表示菌类之比生长速率，则此两个生化反应槽串联之反应系统共有三种型态之稳定状态，本研究对此三种型态之稳定状态和稳定度作深入的分析，对於此反应系统之动态行为，则由电脑运用数值分析的方法及电脑绘图进行分析工作，动态分析的结果显示此生化反应系统之动态行为，以稳定之稳态为主。

In the paper, the steady flow is also included to check the effect on the nonlinear forces with the different wave headings and different side-hull arrangements. From the comparisons of the theory and experiment, we find that the present technique can well predict the added resistance and lateral drifting force for the trimaran ship advancing in waves.

本论文将数值分析之结果与实验值做比较，来验证数值方法分析之正确性，并将稳态项、不同入射波波向以及不同副船体配置的影响加入考虑，来预估三体船在波浪中航行时的附加阻力和横向漂流力，从比较结果可看出本方法预估附加阻力及横向漂流力已有相当不错的结论。

Based on long-term monitoring convergence deformation of Wuqiaoling deep-buried long tunnel, this paper analyzes convergence deformation regularity of two parallel main tunnels. Results show the left main tunnel's convergence obviously exceeds that of the right, because the right main tunnel's construction absorbs the experience of the left main tunnel. Furthermore, authors research on rheology rule of Wuqiaoling tunnel by FLAC(superscript 3D). Numerical analysis result basically is consistent with actual measurement result. Finally, 6 principles to dispose soft wall rock rheology are presented.

首先，在对乌鞘岭深埋长隧道进行长期围岩收敛变形的基础上，分析乌鞘岭深埋长隧道左、右主洞的收敛变形规律，其研究结果表明左线主洞的收敛变形均大于右线主洞，这是由于进行右线主洞施工时吸取了左线施工的经验；然后，利用FLAC(上标 3D)对乌鞘岭深长隧道软弱围岩流变进行数值研究，数值分析结果与实测结果较为一致；最后，提出对软弱围岩流变进行工程治理的6条原则。

Based on long-term monitoring convergence deformation of Wuqiaoling deep-buried long tunnel, this paper analyzes convergence deformation regularity of two parallel main tunnels. Results show the left main tunnel＇s convergence obviously exceeds that of the right, because the right main tunnel＇s construction absorbs the experience of the left main tunnel. Furthermore, authors research on rheology rule of Wuqiaoling tunnel by FLAC^3D. Numerical analysis result basically is consistent with actual measurement result. Finally, 6 principles to dispose soft wall rock rheology are presented.

首先，在对乌鞘岭深埋长隧道进行长期围岩收敛变形的基础上，分析乌鞘岭深埋长隧道左、右主洞的收敛变形规律，其研究结果表明左线主洞的收敛变形均大于右线主洞，这是由于进行右线主洞施工时吸取了左线施工的经验；然后，利用FLAC^3D对乌鞘岭深长隧道软弱围岩流变进行数值研究，数值分析结果与实测结果较为一致；最后，提出对软弱围岩流变进行工程治理的6条原则。

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。