数值稳定性

An extended hyperbolic mild-slope equation, which can take such terms as wind input, bottom friction and nonlinearity of wave into account, here has been deduced into a parabolic one in the form of a series of governing equations described with complex amplitude. It became a complete wave model when integrated with corresponding physical and imaginary boundaries, and can be solved through the improved Crank-Nicholson or the well known Alternating Direction Implicit difference method, both of which can accelerate the convergent speed , expand limitation of the mathematical method and improve the quality of the solution.

本文基于综合考虑底摩阻、风能输入及非线性影响的推广双曲型缓坡方程，将其进行转换，产生一个演变方程，其复振幅控制方程为抛物线性，并采用ADI差分格式、改进的Crank-Nicholson格式及相应的物理和虚拟边界条件进行求解，以提高数值模拟的适用性、数值计算的稳定性、收敛速度及精度。

Took Chongqing Gong-he tunnel as an engineering example and studied the failure mechanism of surrounding rock and the correlation with bolt support system by using the methods of theoretical analysis, modeling test, numerical simulation and in situ test, some helpful conclusions were arrived as follows.Firstly, a new failure criterion for transversely isotropic rock mass was proposed with consideration of bedding plane orientation and major principal stress, and the corresponding algorithm, arrived through VC++6.0, can be easily embedded into the software FLAC3D for the geotechnical calculation.

论文在国家自然科学基金专项基金创新群体基金项目(No.50621403)以及国家自然科学基金重点项目"隧道与地下空间工程结构物的稳定性与可靠性(No.50334060)"的资助下，以共和隧道为示范工程，运用理论分析、物理模型实验、数值模拟和现场测试等手段，对共和隧道大埋深段层状岩体的围岩变形破坏机理、锚杆支护力学效应及围岩-支护结构的变形特征等内容进行了研究，其主要研究成果有：①在总结和探讨国内外学者提出的层状岩体经验型连续介质破坏准则基础上，结合层状岩体力学特性，考虑层面方向和最大主应力方向两个影响因素，提出了共和隧道层状岩体横观各向同性破坏准则；采用汇编语言VC++6.0实现了横观各向同性弹塑性本构关系的算法，并嵌入FLAC3D有限差分数值分析软件接口中实现数值运算。

In Chapter 2, starting from the basic fractional ordinary differential equations,weapply a high order approximation of fractional derivative advanced by Lubich to frac-tional differential equation, construct a high numerical difference scheme to solve thefractional differential equation, present error analysis of the algorithms theoretically,and prove the consistency ,convergency and stability.

接下来的第二章中，首先从基本的分数阶常微分方程出发，对Lubich提出的一个关于分数阶导数的高阶近似，将其应用于分数阶微分方程，构造高阶数值差分格式来进行分数阶微分方程的数值求解，并在理论上给出这一算法的误差分析，证明了它的相容性，收敛性和稳定性。

Based on initial condition, during certain time span, numerical analysis method of differential equation, algebra iteration and optimization method are used to solve response of generalized system and to analyze stability of generalized system.

从初始条件出发，在一定时间长度上，采用微分方程数值积分法、代数迭代和优化方法来求解系统响应，获得非线性广义系统稳定性的数值分析方法。

The first part presents develops of predator-prey systems and gives the model that is investigated in our paper; Chapter 2 presents the results on boundedness of solutions and permanence of system; In chapter 3, we explicitly derive a domain of attraction for the positive equilibrium of system by using Liapunov method; The local stability and the conditions that Hopf bifurcation occurs are obtained in chapter 4; In chapter 5, some explicit fomulae of the direction of Hopf bifurcation and the stability of bifurcating periodic solutions on the center manifold are determined,using normal form and center manifold introduced by Hassard et al; In chapter 6, some numerical simulations are performed to illustrate the analytical results found; Our paper ends with a brief conclusion.

全文共分七章，第1章对捕食-食饵系统的发展背景做了介绍并给出了本文研究的模型；第2章讨论了系统的保持性和解的有界性；第3章研究正平衡点的全局性质，对正平衡点的吸引域进行了精确估计；第4章研究了系统的正平衡点的局部稳定性和Hopf分支存在的条件；第5章利用规范型和中心流形定理得到了一个决定Hopf分支方向、分支周期解的稳定性及其他性质的精确公式；第6章对一个具体模型进行了数值模拟；第7章对全文进行了总结。

Thus, non-negative property is suggested as the criterion of stability. Further, diffusion coefficient is replaced by an artificial one in the finite difference equation to simulate the entropy generation can improve the accuracy of the numerical analysis.

在尽可能满足对流扩散过程数值格式中的输运性或守恒性及稳定性的同时，以扩散熵产仿真为原则的伪扩散系数可有效地提高数值模拟的仿真性，为数值计算中扩散系数的修正提供了一种有效的手段。

However, numerical modeling for nonlinear seismic waves is faced with problems such as steep gradients, shocks and unphysical oscillations. Accordingly, some special treatments have been presented to solve these problems. However, in our knowledge, there is no effective method to overcome these problems by far.

非线性弹性波的数值模拟存在陡峭间断面、数值振荡以及误差的指数级增长等现象而破坏数值解的稳定性、收敛性，能否消减上述现象的不利影响成为制约数值方法有效与否的重要因素。

The presterssed anchor cable frame combined with backwall, drainage is necessary due to longtime sability and permanent utilization.Firstly,according the study of engineering of geology situation of the high slope, the mechanism of deformation failure and the major hazard of the high slope of PanMei is analysed comprehensively.And the whole slope is divided into two different geology enginnering areas:Western slope(1160 section plane -1240 section plane)and Eastern slope(1240 section plane -1320 section plane). The result of 3D numerical simulation is the same as geology judgement. Later,slope cut (1:0.75) is implemented based on the engineering comparison and criterion.Meanwhile, Limit equilibrium method , Monte Carlo Probabilistic slope stability the stability , Sensitivity analysis and Finent element method of for assessing the cutted slope stability is carried out. The result indicates that Western slope is instable, Eastern slope is relatively stable.So much attention should be paid to Western slope.Different reinforcement measures in different areas are given according to its stability and meet economical request. Gravity wall is introduced in accordance with landform in order to prevent small falling at the foot of the high slope ,which will be a threat to the high slope stability. Handling measure is also applied to Eastern slope. At last,FLAC3D numerical analysis shows the feasibility and reasonableness of the handling measure of the high slope.

论文首先研究了边坡的工程地质条件，全面分析边坡的变形破坏机制和边坡的主要地质灾害，将边坡分为西段不稳定边坡区(1160剖面～1240剖面)和东段相对稳定边坡区(1240剖面～1320剖面)，通过三维数值模拟再现了边坡在自重作用下的破坏机制和过程；在此基础上通过工程类比和规范要求，确定按照1：0.75进行放坡处理，并分析了放坡后边坡的稳定性状况，分别通过极限平衡法、蒙特卡洛法概率分析、参数敏感性分析和有限元稳定性计算等多种方法对边坡在各种工况下的进行稳定性研究，计算结果表明，西段边坡较之东段边坡稳定情况差，是边坡支护的关键之处，而东段边坡相对是稳定的；边坡的综合治理措施选用的是框架锚索并结合挡土墙和排水工程，治理设计根据不同区段的稳定性情况采用不同的支护结构，做到了经济合理的要求；在边坡的坡脚设置重力式挡土墙，防治边坡小规模的崩塌，会对上部的锚索支护护造成不利影响，进而影响边坡的稳定；东段边坡的填方区也给出了治理对策；最后通过三维显示拉各朗日有限差分程序(FLAC3D)模拟了高边坡放坡和支护效果，论证了治理措施的有效性和合理性。

For some rock slopes, which have not distinct failure surface, but have complicated structure or load on the top and so on, a stability analysis of this type slopes by finite element method is presented, the failure surface is defined by certain rule or strain zone from the computed model, and then the safety factor of the rock slope is abtained by finite element method and limit equilibrium methodAt last, using ANSYS , a famous commercial finite element analysis software, a example of high-steep slope which is bearing the load of the LongGe Mansion is presented, the stability of this slope is studied, as a paradign the the stability evalution of complicated high-steep slope under the action of load of building , the chapter gives some meritable reference in stability assessment of rock slopes using numerical simulation by three-dimension elastic-plastic finite element.

并用有限单元法建立边坡的具体模型，应用折减边坡岩体参数、逐级施加荷载等与边坡工作环境相似的方法进行模拟计算，根据计算结果，采用一定的判别准则或图形可视化方法，确定出边坡的滑裂面，再采用刚体极限平衡法或有限单元法计算其安全系数；最后，通过某一工程实例，用大型有限元程序对边坡在建筑物荷载作用下的稳定性进行分析研究，并以此作为计算分析复杂高边坡在高层建筑物作用下的稳定性评价的一个范例，在采用有限元弹塑性数值模拟岩质边坡稳定性方面提供一些有价值的参考。

The one-dimensional complete hydrodynamic model for border irrigation based on the hybrid numerical method can obviously increase computational stability and convergence, and effectively improve computational precision and efficiency, and provide a good numerical simulation tool for the design of border irrigation system and performance evaluation.

基于混合数值解法的一维畦灌全水动力学数值模拟方法可明显增强数值计算的稳定性和收敛性，有效提高了计算精度和效率，为开展畦灌系统设计与性能评价提供了可靠的数值模拟手段。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。