A semianalytical solution of the Saint‐Venant equations for channel flood routing

Abstract

A semianalytical solution for channel hydraulic routing has been derived from the Saint‐Venant equations. The Saint‐Venant equations were converted into a nonlinear diffusion equation by introducing the Froude number. Subsequently, the mixing cell method is used to discretize a nonlinear diffusion equation in space, transforming it into a first‐order nonlinear ordinary differential equation where the optimal space interval is obtained to be the same as the characteristic reach length. The nonlinear ordinary differential equation was solved by integration with respect to time to achieve a nonlinear implicit algebraic equation. The resulting implicit equation is practical and easy to program on a computer. This method is based on the results of a numerical simulation using the Lambda scheme which indicates that the Froude number is only dependent on the channel roughness and bottom slope. The method was tested with numerical examples and compared with the Lambda scheme and observed data. The hydrographs produced by this method were of comparable accuracy.