数值方程

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。

Numerical dispersion characteristic and impedance relationship of three dimensional perfectly matched layers are analyzed under finite difference approximation in this paper, respectively, which show that numerical dispersion relationship of PML is different from that of the FDTD equations and the impedance of homogeneous PML medium is the same as that of free space.

本文分别分析了有限差分近似下三维理想匹配层的数值色散特性和阻抗关系，分析表明，理想匹配层的数值色散关系有别于时域有限差分方程的数值色散关系；有限差分近似下，均匀理想匹配层媒质的阻抗和自由空间的阻抗相同。

Chapter 5 to text the numerical method put forward carries on the numerical experiment, special two fractional differential equation problem within biologies carries on the test, the number result enunciation method is valid.

第五章对文中所提出的数值方法进行了数值试验，特别就计算生物学中的两个分数阶微分方程问题进行测试，数值结果表明方法是有效的。

This paper studied a filtering high order numerical method for one dimension constant coefficient hy2 perbolic function. The stability and error analysis show the efficiency of this method. Numerical examples are also given to verify the analysis results.

摘 要 考虑一维常系数双曲型方程的高阶数值解法，引进了一种稳定性过滤算子FN ，最后从理论和数值实验上分析了该过滤算子对数值解稳定性和精度的影响。

Therefore, it is necessary to test the computation results and further modify the computation method based on the comparison between the numerical solution of the linear or non-linear equations and the trial value or the computation results of typical cases.

所以，需依靠对非线性数学方程的数值实验及数值解与试验或典型算例结果的比较和物理特性分析，验证数值计算结果，进一步改进计算方法。

The main results can beexpressed as follows:(1)Based on πtheory, some affected factors about wave forces are given, and therelation between affected factors and wave forces is analysised by experimentalresults.(2) The distribution of wave press at representative time and reflection nature aregiven and their variety charactes are discussed by experimental results.(3)By comparing the wave forces of quarter-circular breakwater and semi-circularbreakwater under the same wave conditions,some approximately wave forcesexpressions of quarter-circular breakwater are given.(4)Based on VOF method to trace water free surface,solve numerical value ofRANS equation,and get the distributions of flow field and wave press ofquarter-circular breakwater at the same time during one period,the mechanism ofwave force is also discussed elementarily.(5) Based on the result that RANS equation of numerical simulation agree wellwith experimental results,a new approach to study hydraulic natures of quarter-circular breakwater is provided.

其主要结论如下：一、通过π定理，确定影响波浪力的无因次参变量，根据试验结果对其影响因素进行分析；二、基于模型试验，给出典型时刻圆弧面防波堤的同步波压分布和反射特性，讨论它们的变化特点；三、通过相同条件下圆弧面防波堤与半圆型防波堤两种堤型试验波浪力的比较，给出了圆弧面防波堤波浪力的近似方法；四、利用VOF法追踪自由水面，数值求解RANS方程，得到圆弧堤堤体周围的流场和压力场，初步分析了速度涡流与压力场的相互影响；五、对比数值分析与试验结果，探讨数值方法研究圆弧面防波堤水力特性的可行性，提供新的研究途径

Aim To study the numerical solving process for the large sparse matrix linear equations. Methods To realize the above aim, program developing language C++, cross list data storage structure, the special method of pivoting and elimination of pivot element were adopted.

大型稀疏矩阵线性化方程组的数值求解问题，广泛存在于工程实践尤其是计算机仿真领域，如水力管网计算 [1] 、电力系统的大型导纳矩阵计算、高阶偏微分方程的数值求解[2 ] 以及铸件充型过程与凝固过程的数值模拟等。

Based on the two phase anisotropic model this paper analyses and presents the dynamic equations of elastic wave propagation, the Galerkin variational equation, and the finite element equation in two phase anisotropic media.

基于双相各向异性介质模型，首先推导了双相各向异性介质中弹性波传播的动力学方程及其Galerkin变分方程和有限元运动方程，然后给出了孔隙弹性波方程的有限元数值解法以及二维双相PTL介质中波场模拟的人为吸收边界条件。

For obtaining the numeral solutions of round elastic plates in axisymmetrical deformation with varying-thickness in nonlinear deformation in the unsteady electromagnetic field and mechanical field,by establishing the equations of motion,the equations of distortion,the equations of Lorentz force,the equations of electronic dynamic mechenical,and adopting iterative method,we gained the nonlinear magneto-elastic calculation method and outcome of current-carrying shell,and gained the influencing degree toward mechanical parameter of varying thickness round ferreous plates in the electromagnetic field and mechanical field.

为了获得内边界固定的环形导电薄板在均布力与横向磁场作用下的变形问题的数值解，通过建立运动方程、变形方程、电动力学方程和洛仑兹力方程，运用迭代法得出了载流板壳的非线性磁弹性的计算方法和结果，以及机械场、电磁场对铁质变厚度圆板各力学参量的影响程度。

To investigate the dynamic stability of a two-degree-of-freedom manipulator as a system,differential equations of motion for this system were established on the basis of the Lagrange equation,and perturbed differential equations with period coefficients were derived for the period motion of this system by applying the perturbance theory.

为了研究两自由度机械手系统的动力学稳定性，基于拉格朗日方程给出了它的运动微分方程，并用扰动理论确定系统周期运动具有周期系数的扰动微分方程；根据F loquet理论对该系统扰动微分方程的平衡点的稳定性进行了分析，并用数值方法研究了平衡点失稳后的倍周期分岔过程。

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。