变步长四阶龙格库塔方法在水文水力计算中的应用

将变步长四阶龙格库塔方法用于水库调洪演算与水面线的计算中。变步长龙格库塔方法,可以有效地避免峰值的错过。以安徽省小水库除险加固工程为例,对该水库采用传统试算方法和变步长龙格库塔方法进行调洪演算和水库溢洪道水面线计算,分别得到了下泄洪水过程线、水位变化过程曲线和溢洪道水面线。结果表明:本方法易于程序设计,精度满足工程要求,可以用于水文水力计算中微分方程的求解。

Application of varying step four order Runge-Kutta method in calculation of hydrologic and hydraulic engineering

A novel method of fourth order Runge-Kutta with variable step is applie in calculating the flood routing and water line in reservoir. In comparison with the traditional trial method through solving hydraulic differential equations,The method can effectively avoid missing the peak.Taking a reinforcement project of a small reservoir in Anhui as an example,the paper calculated flood routing and water line of the spillway by using tradition method and varying step four order Runge-Kutta method and got the flood hydrograph, water level change curve and surface line of spillway.The result showed that the proposed method is easy to program design and meet the precision requirement of engineering,and can be used in the calculation of hydrological differential equation.