显式Runge-Kutta法求解明槽恒定渐变流的稳定性研究  

Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough

作　　者：周斌 ZHOU Bin(Shanwei Water Resources and Hydropower Planning and Design Institute,Shanwei 516600,China)

机构地区：[1]汕尾市水利水电规划设计院,广东汕尾516600

出　　处：《人民珠江》2021年第2期72-76,共5页Pearl River

摘　　要：显式Runge-Kutta法是求解明槽恒定渐变流微分方程的常用算法之一,近年来得到国内一些学者的研究和推广。研究显式Runge-Kutta法求解明槽恒定渐变流方程的稳定性可进一步夯实该算法技术推广的基础。采用多元函数泰勒公式展开明槽恒定渐变流的4阶显式Runge-Kutta方程,略去高阶微量并消去部分项后可得到误差传播方程。误差传播方程显示,用4阶显式Runge-Kutta法求解明槽恒定渐变流微分方程时,缓流流态应从下游向上游推算,急流流态从上游向下游推算,才有可能在取用足够小的计算段长时能保证计算的稳定性。通过典型计算进一步验证了该结论,该结论也可进一步推广至至一般性的显式Runge-Kutta法。Explicit Runge-Kutta method is one of the commonly used algorithms to solve the differential equation of constantly gradually varied flow in open channel,which has been studied and popularized by some domestic scholars in recent years.Studying the stability of explicit Runge-Kutta method to solve the constantly gradually varied flow equation in open channel can further consolidate the foundation of technical popularization.The fourth-order explicit Runge-Kutta equation of constantly gradually varied flow in open channel is expanded by Taylor formula of multivariate function,and the error propagation equation can be obtained after omitting high-order trace and eliminating some items.The error propagation equation shows that when the fourth-order explicit Runge-Kutta method is used to solve the differential equation of constantly gradually varied flow in open trough,the slow flow pattern should be calculated from downstream to upstream,and the rapid flow pattern should be calculated from upstream to downstream,so that the stability can be guaranteed when a sufficiently small length is used for calculation.This conclusion can be further verified by typical calculation,and can be further extended to the general explicit Runge-Kutta method.

关 键 词：水面线 明槽恒定渐变流 稳定性 误差分析 RUNGE-KUTTA法 

分 类 号：O241.81[理学—计算数学]