数值

In the numericalstudy, three-dimensional elastodynamics equations and Morison equation are applied tosimulate the time histories of dynamic response of submarine pipelines suspended over flatbeds sucessfully. The three-dimensional interaction of pipeline and internal flow isnumerically simulated by applying the iterative computation to the fluid-structure interfacesand using the elastodynamic equation and the incompressible fluid N-S equation andcontinuity equation.

在数值研究方面，本文利用三维弹性动力学方程，结合莫里森方程，较好地模拟了规则波浪作用下近壁悬跨弹性海底管线动力响应过程，结合不可压缩流体N-S方程和连续方程，进行管线及其内部流体的三维流固耦合数值计算，基于数值计算结果探讨内流管线系统的动力特性和管内流体特征。

Through adopting frequency-response functions and railway track irregularity PSD, methods and models are optimized. The speed of simulation is enhanced with fast Fourier transformation.

通过引入频响函数及轨道不平顺谱优化了列车荷载数值算法及计算模型，并在数值计算中采用傅里叶快速数值算法，提高列车荷载的模拟的效率和可靠性。

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。

Thus, non-negative property is suggested as the criterion of stability. Further, diffusion coefficient is replaced by an artificial one in the finite difference equation to simulate the entropy generation can improve the accuracy of the numerical analysis.

在尽可能满足对流扩散过程数值格式中的输运性或守恒性及稳定性的同时，以扩散熵产仿真为原则的伪扩散系数可有效地提高数值模拟的仿真性，为数值计算中扩散系数的修正提供了一种有效的手段。

With the development of computer technology and numerical modeling techniques, many numerical methods have been established and applied to this field. Finite element method is one of the most effective.

随着计算机科学和数值计算方法的发展，目前已经有很多数值方法应用于大体积混凝土结构温度应力仿真分析中，其中有限单元法是一种十分有效的数值分析方法。

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。

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。

Using Biot's 2D elastodynamic theory solves the saturated soil equation. The Fredholm integral equation of the second kind can be built by using the fundamental solution of circular load, the compatibility condition and superposition method. The Fredholm integral equation of the second kind of pile groups can be solved by using numerical method. The numerical solutions of pile groups axial forces, pore pressures under vertical harmonic loading and shear forces, moments and pore pressures under horizontal harmonic loading can be obtained.

采用Biot提出的三维波动原理，利用圆形简谐载荷作用下的Biot固结方程的基本解和桩土之间的变形协调条件，并采用叠加原理得到饱和土中群桩的第二类Fredholm积分方程，应用数值法求解群桩的第二类Fredholm积分方程，得到在垂直简谐载荷作用下群桩的轴力、孔压随桩身变化的数值结果以及在水平简谐载荷作用下群桩的剪力、弯矩和孔压随桩身变化的数值结果。

Forexample, the group 2, 4 and 10 of BOX-PCR were good agreement with group 5, 13 and12 of numerical analysis, and the group 3, 4 and 8 of RAPD were equal to group 6, 12and 8 of numerical analysis, and the group 5, 6 and 8 were identical with group 6, 12 and8 of numerical analysis, which indicated the 4 methods used could reveal the biodiversityamong the tested free-living nitrogen fixation strains.

总的来说，本研究所采用的表型分群和遗传型分群的结果在总体趋势上是一致的，BOX-PCR的群2、4和10分别与数值分类中的第5、13和12表观群一致；RAPD的群3、4和8分别与数值分类的群6、12和8相对应，16S rRNA PCR-RFLP中的群5、6和8则数值分类的群6、12和10完全吻合，说明本实验所获得的研究结果可信。

Finite difference method is adopted in this model to analyze the temperature distribution and fulgurite resistance of a fuse.

针对所提出的简化模型，用直接差分法进行数值模拟，设计出用直接差分法进行数值计算的通用程序，实现了温度分布和弧后残躯电阻的数值分析。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新