4阶Runge-Kutta法调洪演算误差传播规律研究  

Research on Error Propagation Law of Flood Routing by Fourth-order Runge-Kutta Method

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7期126-131,共6页Pearl River

摘　　要：4阶Runge-Kutta法是求解水库调洪演算常微分方程的常用算法之一,研究其误差传播规律对提高成果精度有着重大的意义。采用多元函数泰勒公式展开调洪演算的方程,略去高阶微量后可得到各参数误差方程和误差传播方程。结果表明,相对误差幅度相同时,库水位上升期入库流量的误差影响强于出库流量;库水位降落期出库流量的误差影响强于入库流量;库面面积产生的水位单步误差在库水位升、降期的正负号相反,且在最高库水位附近趋于0。对于库水位累积误差,库水位上升期入库流量的误差影响最为显著;库水位降落期入库流量误差的影响逐步减弱,而出库流量的误差影响逐步加强。The fourth-order Runge-Kutta method is one of the commonly used algorithms for solving ordinary differential equations of reservoir flood routing.Studying its error propagation law is of great significance for improving the accuracy of results.The equation of flood routing is expanded by Taylor formula of multivariate function,and the error equation and error propagation equation of each parameter can be obtained after omitting high-order trace.The results show that when the relative margin of error is the same,the influence of the error of inflow during the rising period of reservoir water level is stronger than that of outflow.The influence of the error of outflow during the drawdown period of reservoir water level is stronger than that of inflow.The single-step error of water level caused by reservoir surface area has opposite sign in the rising and drawdown periods of reservoir water level,and tends to zero near the highest reservoir water level.For accumulated errors of reservoir water level,the influence of inflow error during the rising period of reservoir water level is the most significant,that during the drawdown period is gradually weakened,while the influence of outflow error is gradually strengthened.

关 键 词：调洪演算 误差分析 基础数据误差 RUNGE-KUTTA法 

分 类 号：TV697.13[水利工程—水利水电工程]