数值方程

Groove design ; flow line equation ; numerical simulation

槽型设计；流线方程；数值模拟

At present, the common numerical methods are finite difference, finite element , boundary element, integration equation and transmission line method.

目前，解决这类问题的数值方法主要有有限差分法、有限元法、边界元法、积分方程法、传输线法等。

The dynamic behaviour of copper was investgated making use of an ex-perimental Lagrangian analysis technique,in which multiple manganin gauges were used to measure the stress-time history at different Lagrangian positions in the stress wave field,and a modified pathline method was used to analyse and solve the dynamic and physical parameters of the flow field.

对紫铜材料的拉氏实验结果采用改进的路径线法进行拉氏分析，得到了各物理量的流场分布，拟合出了本构方程参数，并由此进行了数值模拟。

From Maxwells equations, the vectorial and scalar wave equations for 3D, 2D and 1D are given out one by one using the slowly varying envelope approximation.

从电磁场的Maxwell方程组出发，分别导出了缓变包络近似条件下矢量及标量波动方程的三维、二维、一维形式，然后对其横向和纵向数值处理方法分别作了介绍。

The finite difference time-domain method is stable and easy to be used, but due to the fact that it approximates the space derivatives in Maxwells curlequations by central difference, FDTD usually requires more than 20 grids perwavelength to achieve acceptable accuracy. As a contrast, pseudospectraltime-domain method approximates the space derivatives by pseudospectralmethod, which guarantees the accuracy, theoretically requiting only 2 grids perwavelength.

传统的电磁场数值算法——时域有限差分法稳定而易于实现，但由于FDTD采用中心差分近似Maxwell旋度方程的微分，每个波长上需要取的网格数通常较多，而时域伪谱法采用伪谱法求微分，理论上每个波长只需要取两个网格便可以达到较高的精度。

Wideangle parabolic approximations to wave equation usually lead to nonconstant differential migrators with their coefficients varying with lateral velocity variations, and hence require a finitedifference numerical implementation.

波动方程宽角抛物逼近得到的通常是非常系数的单程波传播算子，其系数是速度横向变化的函数，因此需要利用有限差分进行数值实施。

The method, based on MNA equations and numerical inversion of Laplace transform, is used for the transient simulation of interconnection circuits with frequency-dependent parameter.

本文运用基于复频域MNA方程的数值反拉普拉斯变换法分析高速集成电路中频变参数互连电路的时域响应。

In this paper we propose a one-dimensional muonic atom model, on which the time-dependent Schrdinger equation is numerically solved by Crank-Nicholson method.

本文提出了一个一维μ介子原子模型，用数值积分方法求解了在超强激光场作用下该模型原子的含时Schrdinger方程，得到了它的高次谐波发射谱。

Based on Stuart et al.'s electron density evolution equation, the electron density evolution process in fused silica film irradiated by short-pulse laser for τ∈[0.015] ps were studied by means of numerical method. The effects of initial electron density N and laser pulse width τ on laser threshold intensity I and damage threshold fluence. F were analyzed respectively.

基于STUART等人的电子密度演化方程，运用数值模拟方法，研究了脉宽为τ∈[0.01， 5]ps范围内单脉冲激光作用下熔融石英薄膜中电子密度演化过程；讨论了初始电子密度、激光脉冲宽度对阈值功率密度和阈值能量的影响；分析了初始电子密度、激光脉冲宽度对多光子离化及雪崩离化的影响。

We use the single particle model and find a new nonlinear resonant acceleration criterion analytical: nw(1)+mw(2)=NW, m,n,Nare integers, w(1,w(2), W are the frequency of the two waves and the charged particle cyclotron respective,this result can be extended to the multiple waves ,we make numerical simulation and numerical results are consistent with the analytical results. This paper consists six chapters.

因此本文从基本的情况开始，以两个静电波与磁化等离子体相互作用问题为研究出发点，通过多标度展开的理论方法，求解带电粒子的运动方程，得到的一个新的非线性共振加速条件：nw(1)+mw(2)=NW，（m，n，N为整数，W，w(1)，w(2)分别为带电粒子的回旋频率以及两个静电波的频率），该结果可以推广到多个静电波作用于磁化等离子体的情况，随后通过数值计算证实了解析结论的可靠性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。