曲线坐标系

In curvilinear coordinates , a numerical simulation model for wave propagation on non-uniform current in water of slowly varying topography was presented with employing self-adaptive grids method.

利用自适应网格技术，建立了曲线坐标系下缓变水深水域非均匀水流中波浪传播的数值模拟模型。

Based on application of 3D body-fitted numerical grid with a curvilinear coordinates system and the theories about turbulent flow and the laminar flow, the new techniques that the independent variables were expressed by co-variable velocities were applied to solve the problems about flow around a high-speed car body for the first time.

采用当今数值新技术，较为全面和深入地研究了高速汽车车身绕流问题。本文依据k-ε双方程湍流模型和附面层理论，采用先进的曲线坐标系下的贴体与边界正交数值网格技术，首次把以协变速度分量作为独立变量的数值技术运用于汽车车身绕流问题的求解。

Based on SIMPLER algorithm in the curvilinear body-fitted coordinates, the calculations were performed for Pr=0.7, Re=10~1000 on non-orthogonal non-staggered grids which are generated by elliptic equation systems.

采用曲线坐标系下压力与速度耦合的SIMPLER算法，数值研究了周期性渐扩渐缩波纹通道内脉动流动与换热情况，流动Re数的范围为10~1000，Pr数为0.7。

A three- dimensional turbulence model in non-orthogonal curvilinear coordinates is proposed to investigate the impacts of vegetation on channel morphology. The model includes vegetation-induced drag force and vegetation density in the control equations to describe the effects of vegetation on flow structure, and solves sediment continuity equation to compute channel geometry.

本文建立曲线坐标系下的三维湍流模型研究水生植物对河道形态的影响，在水流控制方程中加入植物阻力项和植物密度项来描述水生植物对水动力特性的贡献，通过泥沙质量守恒方程求解河道变形，在适体网格中求解模型的控制方程。

Two different hypotheses on the quantization of particle motion in the flat space by curved coordinate systems are discussed, and their differences in physical ideas and practical operations are compared.

徐湛讨论了平直空间曲线坐标系中质点运动的两种不同的量子化假设，比较了它们在物理思想和实际操作上的区别和优劣。

A numerical model based on the surface geometry of the horizontal twisted and fluted tube was established.

本文做的主要工作有： 1。根据水平螺旋槽管的槽道几何形状建立正交曲线坐标系 2。

This project studies the scale-dependent deformation behavior of the metal matrix composite, the void nucleation and void growth mechanisms at the micron/submicron scale. The main results are:(1) In prophase, growth and coalescence of the void embedded in the graded matrix are analyzed in detailed;(2) Based on the infinite solid model containing a micro-void, coupling effects of the void shape and the void size on the void growth are studied carefully, the results show that it seems to exist a critical equivalent void radius, which is associated with the material length. When radius of a microvoid is close to or smaller than the critical void radius, the micro-void growth rate is essentially eliminated;(3) The coupling effects of the particle shape and size on the mesoscopic stress fields within the particle and matrix are also investigated by introducing the conception of inclusion/matrix interfacial energy. The results show that the stress concentration factors within the particle and on the matrix/particle interface are also strongly size-dependent,so the void nucleation mechanism is size-dependent.(4) By employing a specific orthogonal curve coordinate frame and a 'kernel function' conception, a 'unified method'solving the spheriodal and spherical void problems is suggested; by this unified method, size-dependent plastic potentials of the porous materials containing the spheriodal or spherical voids are obtained, which extend the traditional Gurson model for the spherical void and GLD model for the spheriodal voids to the micron scale.(5) Based on the RVE model containing the spheriodal or spherical particles, the influences of the particle shape and size on the size-dependent mechanical behavior of metal matrix composite are studied.

中文摘要：本项目对金属基复合材料在微细观尺度下的尺度相关变形行为、孔洞形核及长大的机理和模型进行了研究，取得了如下主要结果：1）在前期研究中，探讨了基体的梯度分布对孔洞长大和聚合的影响；2）基于含孔洞的无限大体模型，探讨了孔洞形状和孔洞尺寸对其长大的耦合作用，结果表明：可能存在一个与材料特征长度相关的临界孔洞尺寸，当椭球孔洞的等效半径小于临界孔洞半径时，孔洞的长大受到明显抑制；3）通过引入基体/夹杂界面能的概念，分析了夹杂尺寸、夹杂形状对材料细观应力场的耦合影响，结果表明：颗粒内部和界面上的应力集中因子强烈地依赖于夹杂的尺寸和形状，因此，孔洞的形核机理是尺寸相关的；4）采用一种特殊的正交曲线坐标系和引入"核函数"的概念，"统一"地得到了含椭球和球形孔洞的材料的尺寸相关塑性势，它将传统的Gurson球形孔洞模型和GLD椭球孔洞模型推广到微尺度范围；5）基于含椭球和球形夹杂的体胞模型，初步研究了夹杂形状、夹杂尺寸对金属基复合材料尺寸相关力学行为的影响。

Here illustrate by examples on the method of choosing and determining physical base and space metric tensor in arbitrary curvilinear coordinate system, the results show clearly that this algorithm of matrix is correct, and show that the algorithm of matrix is really ...

并用示例说明在正交或非正交的任意曲线坐标系中选择和确定物理基及空间度量张量的方法，所得结果与文献[1]和[2]完全吻合，表明这一方法是令人满意的。

This paper has presented the formulae of calculating physical base and space metric tensor for complicated system, these formulae are developed by using non-Cartesian tensor analysis and introducing physical base.

本文基于非笛卡儿张量的分析，并引入了物理基，提出了复杂系统的空间度量张量的一系列矩阵公式，据以求出任意曲线坐标系中的数学模型。

A method for choicing and determining physical base and space metric tensor in an arbitrary curvilinear (orthogonal and non-orthogonal) coordinate system is illustrated by examples.

通过示例说明，在正交或非正交的任意曲线坐标系中选择和确定物理基及空间度量张量的方法，得到了与以往文献吻合的满意结果。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。