基于MATLAB的明渠恒定非均匀渐变流水面线的数值计算

Numerical calculation of open-channel constant non-uniform gradient flow of water line based on MATLAB

明渠恒定非均匀渐变流的微分方程难以求出其解析解,本文针对底宽渐变的渠槽,采用数值分析中改进的欧拉法和四阶龙格库塔法求出水面线的基本微分方程的数值解,再结合具有强大数值计算功能和作图功能的MATLAB软件写出一类方便调用的库函数文件,方便调用和修改边界条件.此方法对棱柱体渠道也适用.另外,本文还讨论了迭代步长的选择和精度控制的方法.

For the basic equation of surface profile of non-uniform gradient flow,it is difficult to find out its analytical solution.This paper mainly introduces modified Euler＇s method and fourth-order Runge-Kutta method in numerical analysis for bottom width gradually varied channel to make numerical solution of the water profile＇s basic differential equation.Combined with strong numerical computation function and mapping function of MATLAB software to write a class of convenient calls library function files,it is convenient to call and modify boundary conditions.This method is also suitable for prism body.In addition,this paper also discusses the iteration step length selection and precision control method.