三项方程

An adaptive grid scheme controlling cell area is used to generated grids in the divergent section of symmetric annular nozzle, and the generated grids are used in the flowfield calculation through the uncoupled way. The elliptic equations are used to generate grids in three dimensional regions of FDN divergent section, the source terms used in the equations employ a mathematical form which is independent of the boundary shape and of the boundary grid point distribution, the free parameters contained in the source terms are determined by the two restraint conditions, the intersection angle of transverse grid lines with boundaries and the local curvature of the transverse grid lines at the boundaries, and the interior grid distribution controlled directly by the grid point distribution assigned on the boundaries is realized, it makes the grid more clustering near the nozzle wall. For the generated grids in the whole computational regions have a good smoothness and orthogonality, the accuracy of calculation in the flowfield is ensured.

对轴对称的环形喷管采用控制网格面积的自适应网格方法对扩散段部分进行了网格生成，并通过非耦合方式应用于喷管的流场计算中；对强制偏流喷管扩散段内的三维区域采用椭圆型方程进行网格生成，方程中的源项采用了与边界形状和边界网格点分布无关的数学形式，源项内的自由参数由横向网格线与边界的交角及横向网格线在边界处的局部曲率两个约束条件来确定，实现了由边界上的网格分布直接控制内部的网格点，使壁面附近具有较密集的网格，并且在整个计算区域内的网格都具有良好的光滑性和正交性，从而保证了流场计算的准确性。

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

Based on the equilibrium equation of an arch element the cubic nonlinear dynamic model with second order is established and the nonlinear differential dynamic system without constant term is obtained through a transfer process of T=U+b. Hence three fixed points and the homoclinic orbits are found. The critical condition of the chaotic vibration of the elastic arch is given by using the method of Melnikov function. The numerical results of the stationary and chaotic motion are given and discussed.

首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型；然后通过变换使方程转化为不含常数项的非线性微分动力系统，并由此得到无扰动系统的3个不动点与同宿轨道；再用Melnikov函数法给出了发生混沌的临界条件；最后给出了该系统出现定常运动和混沌运动的数值结果。

First, we have proved that the constraint of local constant gradient angles is equivalent to the minimization of total variation. Based on this, a stronger continuity constraint of gradient angle is presented. The interpolation formula (a 3-degree-PDE) derived from the constraint can ensure the continuity of level lines and reduce the width of edges. The contrast invariant of the regularizer of the formula is also proved.

首先证明了局部恒定的梯度角约束插值等价于总变分最小化；在此基础上，提出一个具有更强连续性的梯度角约束，由这个约束条件导出的三阶偏微分方程使插值的图像既可以保证水平线方向的连续性，又减小图像边缘的宽度；最后证明了插值方程中正则项的对比不变性。

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。

Based on the generalized potential energy variational principle of nonlinear elasticity theory with large deflection,the incomplete generalized potential energy functional is established on the space coupling free vibration of three-span self-anchored suspension bridge by considering the effect of coupling of flexural and axial action,and shearing strain energy of stifening girder.

摘 要：基于大位移非线性弹性理论的广义变分厚理，考虑了加劲梁的压弯耦合和剪切应变能的影响，建立了三跨自锚式悬索桥空间耦合自由振动的大位移不完全广义势能泛函，通过约束变分导出了自锚式悬索桥的竖向挠曲振动、横向挠曲振动和纵向振动的基础微分方程，忽略非线性项的影响，进而得到线性振动微分方程。

The nonlinear hyperbolic conservation laws of the transient flow of the media in gas pipeline are hard to he solved, so, the control conservation laws are constituted of mass, momentum arid energy conservation laws, TVD/Godunov hydrid algorithm is used to simulate the transient flow in gas pipeline, and the traditional splitting approach processing nonlinear convection in momentum equation is dismissed ,the convection tern; is directly processed, in the way, the stablization of the algorithm and emulating accuracy of the transient flow are greatly improved.

针对管道中介质瞬变流动的非线性偏微分方程组难以解析求解的问题，由质量、动量、能量三个偏微分方程构成的控制方程组，应用TVD/Godunov混合算法数值模拟天然气管道中气体的瞬变流动，摒弃了传统的差分方法时动量方程非线性时流项的线性化处理，而直接处理非线性对流项，从而大大提高了算法的稳定性和管道瞬变流动的仿真精度。

Based on the source terms and fusion burn-up equations,a three-temperature plasma model is founded in which the electrons,ions,and the radiation filed are represented by separate temperatureskT_e,kT_i and kT_r,respectively,where kT_r is characterized by a Planckian distribution.

第四章建立了考虑α粒子慢化的两温模型和三温模型，首先导出了考虑慢化的α粒子对等离子体的能源项，替换已有的两温模型的等离子体能量密度方程中的能源项，将其改进为考虑α粒子慢化过程的两温模型，与瞬时沉积能量的两温模型作了对比，在不同的初始温度密度条件下考察了α粒子慢化对等离子体聚变燃烧的影响。

In the case that the oscillation factor isn't sign reversal and neutral factor is p, by discussing the sign of the neutral term's first derivative and using Holder inequality the oscillation conditions of the all solutions of this kind of equation are studied, three sufficient theories that all solutions of the equation oscillate are obtained.

在振动因子q保号、中立型因子p的情况下，通过对中立型项一阶导数符号的讨论，根据Holder不等式，研究了该类方程的解振动的条件，得到了所研究方程所有解振动的三个充分性定理，所得结论是对该类问题已有结论的进一步完善和推广。

In this paper, the method of Lyapunov function is used to discuss the stability of the solution of a kind of third order quasilinear differential equation with two nonlinear terms.

应用Lyapunov函数方法讨论一类含两个非线性项的三阶拟线性微分方程解的稳定性，得到了此类方程解的稳定性的若干新结果，同时推广了作者已有的结果。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。