龙格—库塔法计算明渠恒定渐变流水面线

Calculation of Water Surface Profile of Gradually Varied Steady Flow in Open Channel with Runge-Kutta Method

用龙格—库塔法计算棱柱体明渠恒定渐变流水面线,可求得距控制断面任意长度的断面水深,避免逐段试算法产生的系列问题。推导出分别由上游和下游控制断面计算水面线的两种模型,基于龙格—库塔法的Matlab函数ode45计算水面线。算例表明,与逐段试算法相比,ode45的计算结果精度更高,计算水面线的新方法简单易行,便于在工程中推广。

In this paper, Runge-Kutta method was firstly used to calculate gradually varied steady flow in prismatic channel. It can calculate the depth of any section at a distance from the control section, avoiding a series of problems occurred in the piece- wise trail-error method. Two models for calculating the water surface profile were deduced, from control section in upstream and in downstream. One of Matlab functions, ode45, based on Runge-Kutta method was directly used to calculate the water surface profile. Compared with the piecewise trail-error method, the results of shows that ode45 possesses higher accuracy, so that the way of calculating water surface profile is practical and easy to be popularized in engineering.