数值方法

The experimental setup for the turbulent jets in crossflow is designed, and the hot wire anemometry IFA 300 is used to measure the velocity field and the turbulent kinetic energy, and the computational result matches experimental measurement reasonably well. The experimental result is very important in the analysis of the flow field, deduction of the equation of the jet trajectory, check of the turbulence model and validation of the numerical method.

首先，建立了用于测量横向紊动射流的实验台，并利用IFA 300型热膜风速仪系统测量了多种工况下的流场，并将速度、湍动能结果与数值计算结果进行了比较，实验结果与数值模拟结果吻合较好，从而为分析流场特性、确定射流轨迹、比较湍流模型以及验证数值计算方法提供了依据。

It shows that a remarkable advantage of the symplectic methods applied to the Schrodinger equation is the precise preservation of charge conservation law. In order to study the numerical stability, we also adopt the different time step sizes.

为了比较，我们还给出了同阶的非辛算法的数值模拟，从而得到辛摄动配置算法和其在理论上等价的辛龙格-库塔方法在数值上的等效性以及辛算法在数值计算中的优越性。

By using the meshless method, a numerical ocean engineering basin was established to simulate irregular waves propagated in shallow water. Locating the source points outside the computational domain, the problem of water wave propagation was solved by collocation of only a few boundary points instead of meshes.

采用基于配点和径向基函数的无网格数值模拟方法，建立数值海洋工程水池，将源点布置在模拟波浪场之外，沿边界布置配点而不是划分网格；对深水不规则波经斜坡过渡后在均匀水深浅水域中传播的过程进行无网格数值模拟和波谱的迭代修正。

A new method for the generation of curvilinear grid has been proposed. Some curvilinear grid generation examples show that satisfactory grids can be generated for simple-connected regions and connected- regions with complex boundary by using the proposed adjusting factors.

3提出了一种生成边界处正交曲线网格的新方法，收敛速度快，在复杂边界流场区域的数值计算中，有很大的实用价值；为了克服复杂几何边界给数值计算带来的困难，提高通用性以及水流的预测精度，本文采用上述网格生成技术，在直角坐标系三维非恒定明渠紊流的沿层积分数值模型基础上，发展了曲线坐标系下的多层紊流水动力模型。

As a new technique, the manifold method, proposed by Genhua, Shi in 1990s is based on the concept of topology manifold and differential manifold in mathematics.

其中尤以数值流形方法最为突出，以其新颖的数值思想、先进的数值技术得到了学术界的广泛关注。

Second order incident boundary condition on fixed incident boundary is derived for numerical simulations, based on the cnoidal or sinusoidal motions of wave maker paddle, which shows that the prediction with second order incident boundary condition is more accurate than the prediction with first order incident boundary condition. 2 The analytical solution for higher-order Boussinesq equations is derived and its applicable range is discussed. 3 A 2-D fully non-linear numerical model using boundary element method is developed to obtain wave forces acting on rectangular obstacle. 4 The three-dimensional fully non-linear waves are studied in a numerical wave tank using finite element method.The studies on the coupled numerical model combined Boussinesq equations with Laplace equation are following.

非耦合非线性波浪计算模型：1 根据造波板做椭圆余弦运动或正弦运动速度，推导出数值模拟波浪水槽时固定入射边界上的二阶波浪入射边界条件，数值计算结果和实验结果的对比表明采用二阶入射边界条件对波面升高的预报比采用一阶入射边界条件对波面升高的预报更为精确；2 推导了波浪水槽造波板做正弦运动所产生波浪的高阶Boussinesq方程摄动展开解析解，讨论了该解析解的适用范围；3 对整个波浪水槽应用边界元方法数值模拟了波浪对物体的非线性作用；4 用有限元法求解三维Laplace方程模拟了三维完全非线性波浪水槽。

Finally numerical examples with three shape functions are analyzed in detail. The numerical examples show that the modifying generalized moving least squares approximation has high accuracy not only for function value but also one or higher orders derivative.

最后，通过多个数值算例的计算比较了三种形函数的计算结果，结果显示本文提供的MGMLS方法关于函数值和各阶导数值都具有很高的精度。

The discrete velocity ordinate method in the kinetic theory of gases is developed and applied to discretize the correspo

借助非定常时间分裂法和无波动无自由参数的NND耗散格式，建立直接求解微观分子速度分布函数的有限差分数值格式；研究并发展可用于离散速度坐标点选取和离散速度空间宏观取矩的高斯─埃尔米特无穷积分方法、等均间隔的牛顿─柯斯复合积分法、以勒让德多项式的根为积分结点的高斯─勒让德数值积分法，并应用于不同马赫数绕流模拟；通过对不同流域一维激波管问题、二维圆柱绕流问题和三维球体绕流的计算研究，并将计算结果与其他途径得到的研究结果诸如DSMC模拟值、N-S解及有关实验数据进行比较分析，创建了一套能有效模拟稀薄流到连续流不同流域气体流动问题简化的统一数值算法研究框架

The numerical examples show that the modifying generalized moving least squares approximation has high accuracy not only for function value but also first or higher orders derivatives.

数值计算显示本文提供的方法关于函数值和各阶导数值都具有很高的精度。

As an effective method of numerical computation, FEM is widely applied in numerical simulation of metal deformation process.

有限元法作为一种有效的数值计算方法已经被广泛应用于金属成形过程的数值模拟方面，但是有限元分析软件在使用过程中也存在许多问题，例如数值模拟解的精度问题，直接优化设计技术参数的问题。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。