变步长龙格库塔方法在安徽中小水库调洪中的应用

摘要

The traditional principle of flood routing through reservoir method is solving the water balance equation through diagramming and trial method ,which would have heavy workflows ,low efficiency and limitations both on programming flexibility and simulation accuracy .A new method is proposed by combining the water balance equation and flow equation into a first-order ordinary differential equation so as to calculate its numerical solution according to the varying-step Runge-Kutta method and boundary conditions .This method is easy to program and with high precision of calculation . Here ,based on C# ,combined with the 84 regulation in Anhui Province and using the EXcellfor pre-post-processing , the Runge-Kutta method and spline interpolation are applied to a small and medium reservoir flood routing in Anhui .The results show that the Runge-Kutta method can effectively avoid the missing of peak value .The calculation examples show that the proposed method has a high precision and it is applicable to the calculations of small and medium reservoir flood routing .%传统的水库调洪方法原理是通过图解和试算求解相关水量平衡方程，该方法计算工作量大、效率低，在编程灵活性、调算精度方面存在一定的局限性。针对传统水库调洪方法存在的问题，将水量平衡方程与泄流曲线方程归纳成为一个一阶常微分方程，根据边界条件，用变步长龙格库塔方法，求出该方程的数值解。该方法易于程序设计，计算精度高。基于C＃，结合安徽省“84办法”，用EXCEL做前后处理，将龙格库塔方法和样条曲线插值用于安徽中小水库调洪中。采用变步长龙格库塔方法，可以更接近峰值。算例表明，本方法精度高，可以用于安徽中小水库调洪计算。