数值方法

At present, trust region method and line search method are mainly two types of numerical algorithms for nonlinear optimization.

目前，信赖域方法和线搜索方法并列为非线性优化的两类主要数值计算方法。

In order to ensure the reasonable modeling method for thermodynamics model, by adopting these four kinds of models and the reference model, the typical thermodynamics characteristic in drum-the dynamic process of"false level"were dynamically simulated, the results of simulation indicate: The modeling method of considering the changing rates of pressure and volume simultaneously is more reasonable, it's simulation result can be consistent with the result of the reference model, and the numeric error is within±5%, so, this method can be used to build thermodynamics model of drum level.

为确定合适的热力学模型建模方法，采用这四种模型和参考模型，对汽包中典型的热力学性质-"虚假水位"现象的动态过程进行了动态仿真，结果表明：同时考虑汽包体积变化率和压力变化率的建模方法，其动态仿真结果完全可以正确地跟踪参考模型的仿真结果，并且数值误差在5%以内，故该建模方法可以用来建立汽包水位热力学模型。

It is difficult to solve it by traditional mathematic and mechanical methods, so the numerical value analysis is used.

经典的数学方法和力学方法对大多数接触问题都难以解决，需用数值计算方法来进行分析。

In this paper,a new method for estimating the global optimum value in a global optimization problem is proposed .

给出了一种全局最优化问题的全局最优值估计的新方法；该方法通过求一个非线性方程的根使目标函数值逐步减小，因此该方法具有下降算法特征。

Firstly, based on the method of pressure-velocity coupling introduced by SIMPLE algorithm and a revised method of solving the unsteady equation of stream function and vorticity on uniform grid, a special algorithm called primitive-variable-time-dependent approach is formed in the present study. In this algorithm the Navier-Stokes equation in primitive variable form is solved by using the time-dependent approach on non-uniform staggered grid system. The second-order accuracy finite difference is used for the first and second partial derivatives of all variables of the convective terms and diffusion terms.

首先，本文在SIMPLE算法系列处理速度与压力耦合问题的思路和均匀网格下改进的关于流函数涡量方程的数值求解方法的基础上，将非定常原始变量Navier-Stokes方程的求解推广至非等距交错网格剖分，形成了具有本文特色的原始变量时间推进方法，其中对流项和扩散项中各变量的各阶导数均采用二阶精度公式，包括温度在内的离散方程组采用ADI迭代方法求解。

In order to study the numerical method to solve the viscous incompressible flow with free surface, the 3-D mathematical model for steady and unsteady hydrodynamic problem had been established and closed by k-εbuoyant turbulence model. The algebraic coordinate transformation method was used to fit the free surface, the Runge-Kutta method of three step and second precision was devised to simulate the time step. A high precision up-winding compact scheme was studied for the convection term, and the generalized conjugate residual method was set to solve the Poisson equation.

为了研究粘性不可压缩三维问题的数值求解方法，本文从基本的Navier-Stokes方程出发，采用代数拟合方法处理自由表面，用三级二阶Runge-Kutta方法对时间步进过程进行了模拟，并且对对流项的高精度迎风格式进行了研究，给出了求解压力Poisson方程的广义共轭剩余法，从而建立了能够模拟有自由表面的粘性不可压缩问题的定常、非定常三维水动力学模型，并采用k—ε浮湍流模型对其进行封闭。

In this paper, the phase-field models coupled with force flow, shear flow and nature convection are introduced respectively.

阐述了相场方法是凝固过程中对流效应数值模拟的有效方法，分别介绍了考虑强迫对流、剪流、自然对流的相场模型，综述了相场方法在对流领域研究中的应用情况，指出了该研究领域目前存在的问题及今后的发展方向。

In the aspect of the study of the application of HHT method, This dissertation has done three part of jobs: first, the Elcentro strong ground motion which is in common use in earhtquake engineering is analyzed by HHT method, getting its amplitude-frequency-time distribution and the comparison between the HHT marginal spectrum and Fourier spectrum is also made; second, the typical nonlinear system defined by the Duffing equation is analyzed by HHT method, getting its numerical value's amplitude-frequency-time distribution and the comparison between the HHT marginal spectrum and Fourier spectrum is also made; third, define the stationary degree of non-stationary signals making use of 3-D time-frequency spectrum and marginal spectrum, the stationary degree curve of Elcentro seismic recording is protracted according to its defining formula, the stationary degree curve of Elcentro seismic recording which change with time is protracted according to similiar definition.

在HHT方法的应用研究方面，本文做了三部分的工作：首先，利用HHT方法分析了地震工程中常用的Elcentro非平稳强震记录，得到了该记录的振幅－频率－时间分布特性，并将得到的边际谱与傅立叶谱做了比较；其次，应用HHT方法分析了典型的非线性系统－Duffing方程，得到了该方程数值解的振幅－频率－时间分布特性，并将得到的边际谱与傅立叶谱做了比较；最后，利用三维时频谱与边际谱定义了非平稳信号的平稳度，并依照其定义式绘制了Elcentro地震波记录的平稳度曲线，依照类似与依赖与频率变化的平稳度定义，初步尝试编程绘制了Elcentro地震波随时间变化的平稳度曲线。

Stability of 14 high-cut slopes in Guangdong province is analyzed with typical rock mass structure analysis method and stereographic projection method, and with the numerical simulation method UDEC this paper simulated the excavation and reinforcement courses of the important slopes. Some conclutions and suggestions are based the analysis above.

本文结合广东某省道沿线14个高陡岩石边坡的开挖和支护方案的选择设计，运用常用的岩体结构分析方法和赤平投影方法对边坡的稳定性进行了分析，采用UDEC数值模拟方法对一些重点边坡的开挖支护进行了模拟，得出了以下一些结论： 1、边坡支护形式的选择应遵循"安全绿色、水土保持、恢复自然、环保之路"的设计原则。

A practical formula for structural safety classification is derived in the present paper based on Taylor's expansion. It is illustrated to be useful by some examples. Then this practical method is compared with the traditional method

本文利用泰勒展开法推导了结构安全性等级划分的实用公式，通过数值算例验证了该方法的可行性，并将该方法与现行规范中的原有鉴定方法进行了比较。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。