Numerical Solution to Reservoir Flood Routing

Floods spreading through reservoir spillways are usually generalized into a first-order nonlinear ordinary differential equation in engineering. With the classical Runge–Kutta–Fehlberg (RKF) method, ignoring the local stability of the numerical solution, a Runge–Kutta–Fehlberg–Reverse (RKFR) method is advanced and employed to route reservoir floods. In the improved method the step length will further be rectified following the RKF using a local stability parameter, which is based on the fact that as the local truncation error is small enough, the local stability might be approximately characterized by the relative error between the initial dependent variable associated with every step and the feedback that may be calculated through a Runge–Kutta (RK) method. The method presented is first verified with two numerical examples, and the results are more accurate and stable with comparable computed speed compared with the RKF method. Subsequently, the RKFR is coupled with the reservoir flood routing program, and tested with a flood control decision support system of the Huanren–Huilong reservoir group in Hunjiang river basin in Northeast China. The testing results demonstrate that it is more scientific and reliable than the RKF and RK methods.