Nonlinear Convection-Diffusion Equation with Mixing-Cell Method for Channel Flood Routing

Abstract

Using a reference Froude number, a nonlinear convection-diffusion equation was derived from the Saint-Venant equations of continuity and momentum, and was solved by a mixing-cell method. The method involves discretizing the nonlinear diffusion equation in space and transforming it to 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 the fourth-order Runge-Kutta method. The method was tested with numerical examples, and compared with the looped-rating Muskingum-Cunge model and a lambda scheme. The outflow hydrographs produced by this method were of comparable accuracy.