城市暴雨内涝数学模型的研究与应用

Research and application of the mathematical model for urban rainstorm water logging

以城市地表与明渠、河道水流运动为主要模拟对象,研制了模拟城市暴雨内涝积水的数学模型。模型以平面二维非恒定流的基本方程和无结构不规则网格划分技术为骨架,同时,针对小于离散网格尺度的河道或明渠,应用了一维非恒定流方程的算法。采用分类简化处理的方法,将通道分为河道型、路面型、特殊通道型(城市内的二级河道),根据不同类型简化动量方程,求任意网格各个通道上的单宽流量。采用一维非恒定流方程模拟地下排水管网内的水流,并给出泵站、闸门、淹没出流管道等排水系统的处理方法。根据无结构不规则网格的设计思路,按照天津、南京、南昌三市的地形地貌特征分别设计多边形的计算网格。介绍了城市面雨量的计算方法以及数学模型在天津市、南京市、南昌市的应用情况和误差分析。

In this paper, a mathematical model for urban rainstorm water logging is established, the round flow and river flow in the city are the main objects to be simulated. The model is established on the basis of two-dimensional unsteady flow theory and the technique of nonstructural and irregular meshes. A method on the basis of one-dimensional unsteady flow theory is proposed to deal with small scale river. The different discrete forms of momentum equations are derived for different types of passages which are divided into the river type, the ground type and the special passage type (small river in the cities), And the discharge per unit width in each passage of any grid is computed by the different discrete forms of momentum equations. The flow in the drainage pipe network is simulated by one-dimensional unsteady flow theory, and the calculation of the pumping stations, the water gates and submersed pipes is indicated. According to the idea of the nonstructural and irregular meshes, the topographies are considered and the calculation domains that involve any polygon are designed respectively in Tianjin City, Nanjing City and Nanchang City. The application and error analysis of the mathematical model in Tianjin, Nanjing and Nanchang are showed, too.