基于一维运动波理论的坡面汇流和沟道汇流数学模型研究

Numerical Modeling of Overland Flow and Channel Flow based on 1D Kinematic Wave Theory

一维运动波理论常用于坡面汇流和沟道汇流的模拟,根据坡面汇流和沟道汇流的特点,采用不同形式的运动波控制方程组来分别描述坡面汇流和沟道汇流过程。采用Mac Cormack格式开发了坡面汇流模型,采用线性离散和非线性离散的显式有限差分格式开发了沟道汇流模型,通过3个典型的算例对各模型进行了验证。验证结果表明,开发的沟道汇流模型是成功的;空间步长的尺度对数值解精度有较大影响,步长越小,数值解精度越高;在沟道汇流模型中,线性求解和迭代求解两种方法的计算结果基本一致。

One-dimensional kinematic wave theory is often used in the simulation of overland concentrated flow and channel flow. According to their characteristics, the processes of overland flow and channel flow are described by different forms of governing equations. Mac Cormack scheme was used to develop an overland flow model; explicit finite difference schemes with linear discrete and nonlinear discrete method were used to develop channel flow model. Three typical examples were used to test each model. The results demonstrate that the models developed are successful and the scale of spatial interval has great influence on the accuracy of arithmetic solution.Furthermore, the smaller the spatial interval is, the higher the accuracy of arithmetic solution is. In addition, the results of linear solving and iterative solving are almost identical in the model of channel flow.