数值

Traditionally, the numerical simulation studies of gas-solid turbulence flow are based on Reynolds-Averaged models which are not able to get accurate results. While with the rapid development of computer science, direct numerical simulation method becomes more and more vital hotpoint.

传统的研究气固两相湍流数值模拟是基于平均的思想，其无法描述流动的精确结构等缺点让直接数值模拟的方法在这个方面随着高性能计算机的出现而飞速发展。

It gives the related explanations of the experimental results and points out the further studying direction in this field.

将数值模拟结果与理论设计数值进行了对比，表明该计算结果是可信的，计算模型和所生成的网格是合理的。

In this dissertation, research work of near-field numerical simulation is briefly reviewed, some existing problems are analyzed, and the following problems in decoupling numerical simulation, which is a key research direction in present, are studied.

本文简要地回顾了近场波动数值模拟的研究工作，分析了存在的问题，并针对当前的一个主要发展方向—数值模拟的解耦技术，对下列问题进行了研究。

Edge lines are extracted automatically from image, by acquiring points of extremum of first directional derivative vertical with edge line with Fourier transform in frequency domain.

同时，参考一阶方向导数的数值来排除一些非边缘点（一阶方向导数的数值为常数者，零也为常数）。

However, to establish global convergence for these latter methods, one must enforce either sufficient decrease conditions (the Armijo-Goldstein-Wolfe conditions)or a fraction of Cauchy decrease condition - all of which rely on explicit numerical function values, as well as explicit approximations to the directional derivative at the current iterate.

但是，为了保证后面方法的全局收敛，必须有足够的减少条件（Armijo-Goldstein-Wolfe条件）或者部分柯西减少条件——它们全都依赖于外在的数值函数值，就和在当前迭代逼近方向导数一样。

In this dissertation, the author discusses the numerical solution for the direct acoustic scattering problem with the Neumann boundary condition, and pays more attentions to discuss numerical recovering the shape of the obstacle region, which is the inverse problem of the direct acoustic scattering problem with the Dirichlet or impedance boundary condition.

本文重点研究了Neumann边界条价下的声波障碍散射正问题和Dirichlet、Impedance边界条件下的声波障碍散射区域反问题的数值计算方法，得到很好的理论结果和数值结果。

In this paper,regularization method is introduced. The author pays more attentions to investigate the numerical solution for the direct acoustic scattering problem with the Dirichlet boundary condition, and the numerical recovering the shape of the obstacle region which is the inverse problem of the direct acoustic scattering problem with the Dirichlet boundary condition.

本文主要引入正则化方法，研究了针对Dirichlet边界条件的声波障碍正散射问题和声波障碍散射反问题的数值计算方法，并得到了很好的数值结果。

Based on these, a new numerical method for the Dirichlet problem is proposed in this thesis.

本学位论文，正是注意到了这些现象，提出了一种求解Dirichlet问题的新数值方法，克服了以往使用其它数值方法时常常遇到的困难和局限性，显示了分析数学中的问题借助概率理论来解决有着广阔的前景，在理论上和实际中都有着很好的意义。

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。

Based on these, a new numerical method for the Dirichlet problem is proposed in this thesis. This method overcomes the difficulties and limitations resulting from others. It shows that solving problems in analysis by probability theory has a bright future both in theory and practice.

本学位论文，正是注意到了这些现象，提出了一种求解Dirichlet问题的新数值方法，克服了以往使用其它数值方法时常常遇到的困难和局限性，显示了分析数学中的问题借助概率理论来解决有着广阔的前景，在理论上和实际中都有着很好的意义。

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。