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目前常使用的水库调洪方程为时段水量平衡方程,当令时段长△t趋于极小化(即以时间微分dt代替△t)并略去高阶微量时,便得到调洪常微分方程。常用的四阶龙格—库塔(Runge—Kutta)解法不是“A—稳定”的。本文推荐的二次样条函数解法,无论是顺时序还是逆时序调洪,均可获得稳定解,同时,对于水库面积曲线、入库洪水过程线,均以其离散数据用三次样条函数描述,这样更方便于电算程序设计,且描述的精度均高于过去常用的多项式曲线。这种解法既具有连续性的优点,又具有差分方法的计算格式,而且程序仍然是简单的。当假定已知某一标准的入库洪水过程线及最高汛限水位时,通过逆时序调洪样条函数解,便可确定相应的汛期运行水位亦即顺时序的起调水位,便于工程防汛安全管理参考。
At present, the flood regulation equation of reservoir is the time-period water balance equation. When the time length △ t tends to be minimized (that is, the time differential dt instead of △ t) and the high order trace omitted, the ordinary differential equation . The commonly used fourth-order Runge-Kutta solution is not “A-stable”. The quadratic spline function method proposed in this paper can obtain a stable solution both in time sequence and in reverse time sequence. At the same time, for the curve of reservoir area and the course of flood, all the discrete data are described by the cubic spline function , This is more convenient for computer program design, and described the accuracy is higher than the past commonly used polynomial curve. This solution not only has the advantages of continuity, but also has the calculation method of the difference method, and the program is still simple. When it is assumed that a certain standard storage flood process line and the highest flood limited water level are known, the corresponding flood season operation water level, that is, the clockwise sequence water level can be determined by solving the inverse time series flood spline function, which is convenient for the project flood prevention Safety Management Reference.