基于Runge-Kutta法和外推法的水库调洪演算

Analysis of Reservoir Flood Routing Based on the Methods of Runge-Kutta and Extrapolation

为了解决数值解析法步长对水库调洪演算成果精度的影响问题,提出了R-K外推法,即采用精度更高的Runge-Kutta英格兰法与外推法相结合的方法,使计算精度达到甚至优于其他数值解法的精度,并采用拉格朗日插值法解决了实际最高水位一般不落在离散解上的问题,得出精度更高的调洪演算成果。调洪演算实例表明该法可以满足工程实践的要求。

To solve the problem of the impact that the step of numerical-analytical method impacts the accuracy of results,proposing extrapolation R-K that is the more accurate method,that R-K England method and extrapolated method are combined,whose accuracy achieve even better than the other numerical solution.Using Lagrange interpolation solved the problem that the actual highest water level generally does not fall on the discrete solution and obtained Flood results with higher precision.Flood routing example proved the method can satisfy the requirements of engineering practice.