【作者】 向波；

【导师】 槐文信；

【作者基本信息】 武汉大学 ， 水力学及河流动力学， 2004， 硕士

【摘要】 随着计算机技术的飞速发展,人们在研究渗流问题时,越来越多的采用了数学模拟,研究对象也由一维问题逐步发展到二维以及三维问题。迄今为止,已有大量的文献介绍建立在透水或不透水地基上的土坝渗流计算方法。这些方法解决了不少实际的问题,但也不同程度地存在缺陷。本文研究利用有限分析方法,对二维渗流模型进行了数值模拟;为解决有限分析方法在处理边界问题上的弊端,提出了有限分析五点格式,并推导出适合于非稳定均质渗流的有限分析五点格式,提高了有限分析方法的适用性。 本文共分为六章,各章主要内容如下: 第一章为绪论。首先提出了渗流计算中的问题以及主要数值计算方法的研究现状、渗流问题数值模拟的发展方向、对目前存在的主要技术难点作了较系统的阐述,在此基础上结合水利工程的实际需要提出了本文的主要工作内容。 第二章为渗流数学模型及定解条件。文中给出了描述渗流运动的基本方程以及基本方程的初始条件和边界条件,并针对于每一种具体的渗流模型给出了初始条件和边界条件。 第三章为数值方法的描述。给出了三种数学方法的基本描述,分别为有限差分方法、有限分析方法、有限元方法,并且给出了几种方法在渗流计算中的具体格式和格式的具体应用。 第四章为非规则区域中的有限分析五点格式。介绍有限分析五点格式,并通过数学形变,推导出适用于非稳定均质渗流问题的有限分析五点格式。 第五章为工程应用。使用有限分析五点格式,对湖南省岳阳市附近金凤水库渗流进行数值模拟,并取得了很好的结果。 第六章为结论与展望。对本文工作进行总结并对今后的工作进行展望。更多还原

【Abstract】 With the rapid development of modern computer science, more and more people use numerical simulation to study the seepage problem. The 2-Dimension and 3-Dimension case are put forward instead of 1-Dimension case. Lots of articles have introduced the calculation method of earth dam seepage with pervious ground base or impervious ground base so far. Many practical problems are solved with these methods and there are also some disadvantages of these methods in solving the practical problem. In this paper, the Finite Analytical Method is used to simulate the 2-D seepage flow. The traditional 9-point Finite Analytic discretization is used only on the rectangular element. To solve the irregular domain problem, the triangular element which includes only five nodes is applied in this paper. The 5-point scheme of finite analytic method is established to simulate the unsteady seepage flow, which broadens the usage of the Finite Analytic Method.This paper can be divided into six chapters. Here is the brief presentation of each chapter:Chapter 1 is introduction. The up to now synthetically evaluation is given on the research ways and conclusions about main problem in seepage flow simulation. Considering the shortage of the previous research ways and techniques, the research way is draft out in this part. The main research content is introduced based on the practical request of the hydraulic engineering also.Chapter 2 is seepage numerical model and boundary condition. The basic motion equation and initial condition and boundary condition are given. For each seepage model, the boundary condition and initial condition are given also.Chapter 3 is numerical method description. Three numerical methods (FDM, FAM, FEM) are introduced. The detailed calculating scheme and application are given also.Chapter 4 is the 5-point Finite Analytic Schemes in irregular domains. The development of 5-point Finite Method for use on the triangular cells is devoted. The 5-point scheme for unsteady seepage flow is established.Chapter 5 is the project application. The 5-point scheme of Finite Analytic Method is used to simulate the Jinfeng Reservoir dam seepage. It shows good result by this method.Chapter 6 is the conclusion and prospect. It sums up the research ways and according results, points out the prospects study in the future.更多还原