【作者】 张莉；

【导师】 徐小明；

【作者基本信息】 河海大学 ， 应用数学， 2007， 硕士

【摘要】 二维明渠水流数学模型的研究与运用己有相当长的历史，许多成果己经应用到水利、环境、港口航道等工程领域中，为工程的规划设计、施工及水域的可持续发展提供了重要的指导作用。随着国民经济的发展，更多的江河水力资源得到了开发利用，对明渠水流数学模型也提出了新的要求，同时也为水流运动基本理论研究的发展提供了一个很好的机遇和条件，以便明渠水流模型能够更好地服务于生产实践。本文利用边界拟合坐标技术生成正交曲线网格，基于此网格系统，建立平面二维明渠非恒定流的数值模型，实现复杂边界明渠水流的数值模拟。主要研究内容如下：1、采用边界拟合坐标技术建立二维正交曲线网格以克服由于复杂边界而引起的计算困难。提出了一种经济、有效的滑动边界处理方法，提高网格边界上的正交性。2、利用张量分析的方法，推导出正交曲线坐标下二维浅水方程的具体形式。3、采用有限差分法对二维浅水方程进行离散，利用交替方向隐格式法(Alternating Direction Implicit Method简称ADI法)实现在计算区域内对二维浅水方程的求解。将得到的数学模型用于长江南通河段进行算例验证，验证结果比较令人满意。针对紊动粘性系数ε这个重要参数，对该算例进行分析验证，验证结果表明模型中考虑ε结果更好。4、在得到的数学模型中分别加入迭代的思想和迎风格式，以此对模型进行修正。实际算例表明修正是合理的，有助于提高模型的计算精度。更多还原

【Abstract】 The research and application of two-dimensional open channel flow mathematical model has been a long history, and many researches have been applied to such projects as water conservancy, environment, port and channel, flood defense, which plays an important guiding role in the design and construction for a project and sustainable development of waters. With the development of national economy, more hydraulic power resources have been further exploited and utilized, which makes a higher demand for open channel flow mathematical model. Meanwhile, it also provides a good chance and prerequisite for the development of fundamental research of water current and gives a better service to the production practice. This thesis is going to establish a horizontal two-dimensional mathematical model of unsteady open channel flow under curvilinear coordinate system on the basis of the proposed boundary-fitted coordinate technology and try to obtain the flow fields with complex boundaries. The research details of the thesis are as follows.1. An orthogonal curvilinear gird has been established by employing the boundary-fitted coordinate technology, which aims to overcome difficulties of numerical simulation resulting from complex boundary. Besides, an economical and effective sliding boundary processing method of improving the orthogonality of the boundary has been proposed.2. By means of tensor analysis, shallow water wave equations of two dimensional unsteady channel flow in orthogonal curvilinear coordinates have been deducted.3. In the computational domain, shallow water wave equations of two dimensional unsteady channel flow have been dispersed by finite difference method and solved by the alternating direction implicit technique. The established mathematical model mentioned above is applied to test and verify Nantong section of Yangtze River, the result of which proves to be satisfactory. And if it is testified by the eddy viscosity coefficient, the result turns out to be much better.4. Iteration method and upwind scheme have been respectively added to the mathematical mode mentioned above to modify the model, and the result of which proves to be reasonable and helpful to improve the computational accuracy of the model.更多还原