柱坐标

在矢量分析范围内给出2a的一种较好定义，并推导出2a在任意正交曲线上标系，特别是柱坐标系、球坐标系的表达式。

Within the scope of vector analysis , we give a better definition of 2a , and derive the expressions of in any orthogonal curvilinear coordinate system , especially in cylindrical and spherical coordinate systems .

这是很好的练习，在柱坐标下再算一次，看看结果一不一样。

A good exercise : do it in cylindrical and see if you get the same thing .

一类周期对称问题的柱坐标FEM解法

Cylindrical coordinates FEM solution to periodic symmetric problem with a rotating center

柱坐标系下FDTD算法的吸收边界条件

An Absorbing Boundary Condition for the FDTD Equations in the Cylindrical Coordinate

柱坐标系下上随体Maxwell流体模型

Constitutive Model Equation of Upper - convected Maxwell Fluid in Cylinder Coordinate

柱坐标系下OldroydB流体模型

Constitutive model equation of Oldroyd B fluid in cylinder coordinate

弯曲波导中基于PML边界条件的柱坐标广角BPM

Cylindrical Coordinate Wide-angle BPM with PML Boundary Condition in a Bent Waveguide

我们推导出柱坐标系中描述该波的非线性耦合方程组，求出一类不同于在笛卡尔坐标系中得到的偶极旋涡（vortex）的新解。

We have found a new solution of the system , which is different from the dipole vortex obtained in a plane geometry .

三维柱坐标系下PML的实现及近场&远场转换

Application of PML in 3D cylindrical coordinates and near-field to far-field conversion

我们知道，柱坐标中z坐标还是，而x、y坐标，我们用R和θ来表示。

OK , so you know about cylindrical coordinates z where we have the z coordinates stay z , and the xy plane we do R and theta polar coordinates .

介绍一个柱坐标系下非均匀FDTD网格生成系统，实现了网格图形的可视化。

In this paper a Non-uniform FDTD Mesh Generation System in Cylindrical Coordinate is introduced , which can visually generates FDTD grids .

从柱坐标系下NS方程出发，采用SIMPLE算法，结合混合有限分析法，数值模拟了旋转Couette流失稳后的泰勒涡的流动。

Taylor vortices were calculated numerically by employing SIMPLE algorithm and hybrid finite analytic method based on N 、 S equation in cylindrical coordinate .

为了降低维数，x、y的二维空间坐标用柱坐标的径向距离代替，其波数通过汉克尔变换求得。

To reduce the dimensions , radial distance of cylindrical coordinates replaced 2 D spatial coordinates ( x , y ), and the radial wavenumber is obtained by a Hankel transform with respect to radius .

PML在三维柱坐标系下的应用及脉冲天线数值模拟

Application of Perfectly Matched Layer ( PML ) in Three Complex Dimension Coordinates and the Radiation Simulation of Pulse Antenna

通过变分运算得到了柱坐标系下的状态向量方程，该状态向量方程也是Hamilton正则方程。

The state vector equation is derived from the present variation algorithm after performing variation operations , and the state vector equation can be also called Hamilton canonical equation .

利用柱坐标系下的二维PIC程序对金属靶背向超热电子束的运动特性进行了模拟，研究了超热电子的回流机制。

The kinetic features of super hot electrons emitting out of the rear side of metal target is simulated and the reflux is studied by a two-dimension PIC code in cylindrical coordinates .

用Boussinesq近似下的轴对称径向二维柱坐标系中的线性扰动方程组，讨论了圆形大气涡旋系统中扰动的惯性重力不稳定和对称不稳定。

Inertia-gravitational instability and symmetric instability of the disturbance in circular atmospheric vortex systems are discussed by using linear perturbation equations in a two-dimensional axisymmetric cylindrical coordinate under Boussinesq approximation .

柱坐标系下PML-FDTD及总场-散射场区连接条件

The Study on PML-FDTD and Boundary Connecting Conditions of Total-Scattering Fields in 3-D Cylindrical Coordinates

一种方法是借助于Laplace变换及其微分性质，并将坐标原点选在荷载影响范围以外足够远的地方，在直角坐标系下实现了与柱坐标系下类似的求解方法。

One is similar to the method of the cylindrical coordinate system , with the help of Laplace transform and its differential properties and putting the origin of coordinates to a point enough distant from accessional loading .

PML-FDTD及总场散射场区连接边界条件在三维柱坐标系下的实现及应用

Implementation and Application of FDTD and Connection Boundary Conditions of Total-Scattering Fields in 3-D Cylindrical Coordinates

先是考察将热单轴各向异性材料在连续调制光辐照下，在柱坐标系下建立光热辐射测量（PTR）技术的三维理论模型。

At first , the 3-D theoretical model of photothermal radiation was built in the cylindrical coordinate axes , by reviewing thermally uniaxial materials irradiated by continuously modulated beam .

分别用狭义和广义相对论解出了爱因斯坦转盘上的热平衡流体系统内固有温度对柱坐标的依赖关系T0（ρ）。

The dependence of proper temperature on cylindrical coordinates T_0 (ρ) in thermal equilibrium of a fluid system on Einstein turntable is solved by special and general relativity separately .

在柱坐标系下用Hankel积分变换方法求解一般形式的热传导方程得出了直流温升和交变温升空间分布的积分表达式。

Integral expressions for steady-state and time-varying temperature distribution are obtained through solving the heat conduction equation in the most general form in a cylindrical coordinate system by using Hankel integration transformation method .

在均匀格点的基础上，给出了基于柱坐标的全矢量非均匀格点有限差分方法（FDM），并采用了完美匹配层（PML）边界条件。

A general formula is derived for a finite-difference method ( FDM ) with non-uniform grids in a cylindrical coordinate system , and a perfectly matched layer ( PML ) is used for the boundary treatment .

本文使用柱坐标系下的正压浅水方程组以及斜压扰动方程组，分析得出台风涡旋系统中的涡旋Rossby波划分为两种类型。

Based on analysis through barotropic shallow-water equations and baroclinic disturbance equations in the column coordinates , we achieve the results that the vortex Rossby Waves ( VRW ) of a typhoon are separated into two kinds .

文中首先推导了三维柱坐标系下完全匹配层（PML）的差分表达式，并给出保证其解稳定性的更为严格的时间步长公式。

Firstly , The perfectly matched layer ( PML ) in three dimension stretched cylindrical coordinates is deduced , and a strict formula of time step is presented so as to ensure the stability of the numerical solution .

以柱坐标下的半矢量波动方程为基础，采用基于完美匹配层（PML）边界条件的有限差分方法，对弯曲波导进行模式求解，进而得到波导弯曲引起的辐射损耗。

Based on the semi-vector wave equation under cylindrical coordinate system , the mode distribution and complex propagation constant in bent waveguides were computed by a finite difference method with perfectly matched layer ( PML ) boundary condition .

管外用比较严格的柱坐标系下能量守恒方程加以描述，得到一个积分-微分方程组，然后在一定的简化条件下，用Monte-Carlo法及差分法求解此积分-微分方程组。

An energy-conservation model using cylindrical coordinates in the form of integral and differential equations is used for describing the radiative and convective heat transfer in a combustion chamber . The Monte Carlo method and the difference method are used for solving the energy equation .

其中，从柱坐标系下的Navier-Stokes方程和连续性方程出发，建立导叶式旋风管分离柱内旋风流场涡旋流动的精确解，采用无粘性流体假设，对于流场内部进行较为全面的求解。

Starting from Navier-Stokes equations and continuity equation in cylindrical coordinates , the exact solution of flow in the separation space of swirl tube is presented assumed on the condition of inviscid . And the CFD methods is used to investigate the gas flow characteristics .

根据流体体积分数的定义，在直角系Youngs算法的基础上，通过引入修正系数，可以方便地实现Youngs算法在轴对称柱坐标系中的应用。

Based on its algorithm for Cartesian coordinate systems , definition of the function of volume of fluid and a revised coefficient are introduced , and Youngs ' method is developed for axisymmetric coordinate systems .