一种基于求解积分方程的高精度调洪演算方法研究  

Research on a High Precision Reservoir Flood Regulating Calculation Based on Solving Integral Equation

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》2020年第10期75-80,共6页Pearl River

摘　　要：水库调洪演算可分为求解常微分方程和求解积分方程2种方法,其中求解积分方程方法在工程上运用更为广泛。目前工程上广泛使用求解积分方程方法多采用梯形法计算出库水量,使出库流量的计算精度相对偏低,对成果精度有一定的影响,可以研究加以改进。利用调洪积分方程和调洪微分方程,构建3次Hermite多项式拟合出库流量过程,再通过Simpson积分法计算出库水量,可构建出新的水库调洪积分方程,新方程中出库水量的计算结果可达到3次代数精度。新的水库调洪积分方程及其派生的误差传播方程在原方程的基础上增加了3次Hermite多项式拟合的影响项,是传统水库调洪积分方程的一种改进。采用不同的调洪时段对工程实例进行调洪演算,结果表明新方程对计算精度有一定的改善作用,可供工程技术人员参考使用。Reservoir flood regulating calculation can be divided into two methods:solving ordinary differential equation and solving integral equation,of which the method of solving integral equation is more widely used in engineering.At present,trapezoidal method is widely used in engineering to calculate the outflow volume,which has relatively low calculation accuracy of outflow volume,a certain influence on the accuracy of results and a space for improvement.With flood regulating ordinary integral equation and differential equation,cubic Hermite polynomial is constructed to fit the outflow process,outflow volume is calculated by Simpson integral method,and a new reservoir flood regulating integral equation can be constructed,through which the calculation result of outflow volume can reach cubic algebraic precision.The new reservoir flood regulating integral equation and its error transfer equation add the influence term of cubic Hermite polynomial fitting to the original equation,which is an improvement of the traditional reservoir flood regulating integral equation.After the flood regulating calculation is conducted for engineering at different flood regulating periods,the results show that the new equation has certain improvement on calculation accuracy,which can be applied by engineering technicians for reference.

关 键 词：调洪演算 HERMITE多项式 误差分析 

分 类 号：TV122.5[水利工程—水文学及水资源]