数值方法

There are several examples of the advection, hyperbolic system and wave problems discussed in this present work.

数值结果皆与解析解或数值解比对结果良好，证明本文所提出的无网格数值方法对於波动问题具有高度精度、一致性与效率。

The unique advantage of this halfanalytical numerical method is that the analytical process of Conformal Mapping can transform an irregular area into a regular one such as a rectangle. Therefore, the discretization error of numerical methods on the boundary can be avoided, and the numerical algorithm can be implemented more easily, with the computing efficiency improved.

这种保角变换的半解析数值方法的突出优点是：利用前期的保角变换解析处理将不规则的场域转化为规则的矩形域，从而避免了纯数值技术对复杂边界的离散化误差，降低了后期数值计算的算法复杂度，并提高了计算效率。

The numerical results show that our non-reflecting boundary condition and numerical methods are effective.

数值试验的结果表明，本文提出的无反射边界条件和数值方法均很有效。

In this mathematical model, we made the comprehensive consideration of the condensability of the liquid, the Westphal＇s effect, the continuous flow condition and the dynamic property of the ball valve.

应用数值方法建立了自动球阀运动规律的计算机仿真模型，通过数值模拟，得到各个参数对球阀运动动力特性影响的基本规律。

Keywords: Delay differential equation;Numerical method;Numerical stability

中文关键词：延时微分方程；数值方法；数值稳定性

In Chapter 1, the present conditions of numerical methods for the Dirichlet problem, the probability theory which connects with the Dirichlet problem, and the essence and characteristics of the probabilistic numerical method are summarized.

第一章综述了Dirichlet问题数值解的现状、与Dirichlet问题密切联系的概率理论以及概率数值方法的实质和特点。

The numerical study is carried out for a KVLCC2 tanker. Firstly, for the ship in oblique motion in deep water, determination of the computational domain, check of the grid dependence and selection of the turbulence model in numerical simulation are investigated. The effectivity of the numerical method is validated by comparing the numerical results with experimental data published in literature and the experimental results obtained by oblique towing test in the towing tank of Shanghai Jiao Tong University.

以KVLCC2大型油轮为研究对象，首先对船舶深水斜航运动粘性流计算中计算区域的确定、网格依赖性的检验以及湍流模型的选取等问题进行研究，通过将本文数值计算结果与他人的试验结果和在上海交通大学拖曳水池进行的船模斜拖试验结果相比较，验证了本文数值方法的有效性。

Sobolev equation is widely used in many areas, such as hydromechanics, thermodynamics and so on.

中文摘要： Sobolev方程是在流体力学，热力学等领域应用广泛的一类方程，其有限元数值方法研究已有很多工作，如[5]中提出了位移有限元法，[9]中建立了特征混合元方法，[7]提出了H1-Galerkin混合有限元方法，[10]中提出了最小二乘混合元方法。

Furthermore, a strategy of precise orbit determination for lunar satellites is presented, which combines analytical and numerical methods. It is assessed to be reliable and practical.

在此基础上，建立了一种数值方法和分析方法相结合的月球卫星精密定轨方法，并以仿真计算证实了方法的可靠性与应用前景。

In the couping solution, based on the characteristics of the models in this dissertation, each of loading step is finished in unit time. Thus the volumetric strains on the current increment step as analysis parameters are inserted into the equation of continuity and a physical equation for pore water pressure is presented. The fundamental solutions of two kinds of classic problems (axial symmetry and plane strain) are derived. By use of the fundamental solutions of pore water pressure combined with finite element method of soil mechanics, a semi-analytical and semi-numerical method for nonlinear consolidation equations is presented.

在耦合分析中，根据本文模型的特点，将每一荷载增量步看作单位时间完成，对应当前增量步的体变分量作为分析参数代入连续方程，建立了基于数值模型的孔压变化方程，根据工程中最常见的两类问题推导出基本解，结合土骨架的控制方程建立了此类液-固耦合问题的半解析半数值解答体系，编制了有限元程序，从而实现了从建立本构关系到模拟固结问题的全数值方法。

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。