Abstract : variations of flow pattern , flow velocity in deep poo l and side bar , mainstream thread , and water surface , caused by excavation project , are investigated by two - dimensional mathematical model in an orthogonal curvili near coordinate system . the change of bed - load transport rate , and redeposition r ate are predicted . the influences of the excavation project on navigation are ana lyzed . grid - type and flat - type excavation alternatives are proposed and discuss ed 文摘:采用正交曲线坐标系下的河道平面二维数学模型，研究了嘉陵江何家碛边滩采砂后河道流势、流态、滩槽流速、主流位置、水面高程及比降的变化规律，预测了采砂方案完成后卵石推移质输沙率变化及其对航道的影响，并对格形开挖和平整开挖方案进行了比较分析
First , the fundamental theory of the basic fdtd method and its application in the analysis of the electromagnetic properties of infinite planar periodic structures is summarized . the basic ideas of the auxiliary fields fdtd method is expressed and generalized to the situations of the 2 - d periodic structures , to lossy media , and to the curvilinear coordinate . the shortcoming of this method in the management of conformal grids is pointed out 首先总结了fdtd方法的基本理论及其在周期性结构电磁特性分析中的应用，阐述了辅助场fdtd方法的基本思想，把它推广到二维周期性的情况和计算区域为有耗媒质的情况，再进一步推广到曲线坐标系中，并指出了该方法在网格共形处理中的不利之处。
By use of the relationships between the hermite polynomial and the laguerre polynomial , the eigenequations of one - dimensional harmonic oscillator and hydrogen atom are conversed into the same equations in form . therefore the relationships between energy levels and wave functions of one - dimensional harmonic oscillator and hydrogen atom are found . through the coordinates transform , the relationships between energy levels and wave functions of two - dimensional harmonic oscillator and hydrogen atom are found 首先综述了谐振子与氢原子的基本理论的研究现状，并在此基础上对谐振子与氢原子的关系展开了研究，通过厄密特方程与拉盖尔方程的相互转化，将一维谐振子与一维氢原子的本征值方程转化为相同形式的方程，从而比较得出它们能量及波函数间的关系，并通过坐标变换将直角坐标系下二维氢原子的本征值方程转化成与曲线坐标系下二维谐振子的本征值方程相同的形式，从而得出二维氢原子与二维谐振子的能量及波函数的关系。
A normal transform is introduced , and there are enough much grids in the region between the critical layer and the wall , where the variation of the disturbance is the quickest . the finite - difference of governing equations with fourth - order accuracy in the normal direction is utilized in full regions including points close the wall , and is very important for accurately discreting equations . the combination of global and local methods is implemented , and a new iterative formula is derived 对于曲线坐标系下的抛物化稳定性方程,文中发展了求解的高效数值方法:引进法向变换,使得在临界层与壁面之间的扰动量变化最快的区域有更多的法向网格点;导出包含边界邻域在内的完全四阶精度的法向有限差分格式,这对方程精确离散至关重要;采用全局法和局部法相结合的方法及其新的迭代公式,大大加速收敛并得到更精确的特征值。
Finally , in orthogonal curvilinear coordinate systems numerical model is established and applied in the yangtze river estuary in which some regulation plans are taken include submerged jets and groins . verifications are also done to verify water level and velocity . flow fields are computed for the analysis of effect of regulation engineering on the whole water area 最后，应用正交曲线网格技术，建立了正交曲线坐标系下广义浅水方程的计算模式，将之应用于长江口深水航道整治工程的流场计算，进行实测水位、流速验证和流场模拟。
The expression of the improved boussinesq equations in curvilinear orthogonal coordinate system is derived . on the basis of poission equation conversion , the methods to generate curvilinear orthogonal grids are introduced , and then the two - dimensional numerical wave model under curvilinear orthogonal coordinate system is established 推导了正交曲线坐标系下的改进型boussinesq方程，以poission方程变换为基础，建立拟合正交曲线坐标系下正交曲线网格的生成方法，进而建立正交曲线坐标系下的二维波浪模型，提高了模型对复杂地形的适用性。
Based on the review , the fluid flow and heat transfer in the curved circular and rectangular pipes have been researched by employing perturbation method and numerical simulation with a physical model under the rotational orthogonal curvilinear coordinate in a rotating curvilinear pipe with multi - parameters . we firstly analyzed the fully developed fluid flow and heat transfer , mixed convection heat transfer , the development of flow and heat transfer in the inlet in different cross section ( circular , elliptical , annular and rectangular crossection ) . the variations of the secondary flow , axial velocity , distribution of temperature , the friction force on the wall , the ratio of friction factor as well as the nusselt number with different dimensionless parameters had been examined in detailed 本文在总结和分析了一个世纪以来有关曲线管道流动和换热特性的研究成果的基础上，以旋转正交曲线坐标系统下的多参数旋转螺旋管道中的对流传热为物理模型，通过摄动方法和有限体积法，首次对各种截面(圆截面、椭圆截面、环形截面、矩形截面)旋转曲线管道内充分发展流动的流动结构和传热特性(包括耦合对流传热特性)以及旋转曲线管道开口段发展流动的流动结构和换热特性进行了系统的数值模拟和理论分析，详细讨论了各种无量纲参数对管道内轴向速度分布、二次流结构、温度分布、壁面摩擦力、摩擦系数比以及管道nusselt数的影响，获得了若干创新性成果。
In arbitrary curvilinear coordinate systems , three dimensional turbulent combustion flow fields of the three kinds of turbofan engine afterburner with the longitudinal heat shield 、 outer cold flow and the jet nozzle are simulated . the three - dimensional body - fitted grids are generated by an elliptical grid generation procedure and zone method 本文在任意曲线坐标系统下对三种带有纵向隔热屏、外冷却通道和尾喷管的涡扇发动机加力燃烧室的三维紊流燃烧流场进行数值模拟。
