Numerical evaluation of the general flow hydraulics and estimation of the river plain by solving the Saint–Venant equation

Abstract

Continuity and momentum equations govern the movement of unsteady flows in open channels, known as Saint–Venant equations. Numerical models of flood routing are classified according to the simplifications made in these equations. Among the flood routing methods, one can refer to dynamic wave and kinematic models and the Att-Kin and Muskingum hydrological models. The kinematic-wave model solves the Saint–Venant equations approximately by considering the gravity and the frictional force terms. This method assumes that the slopes of the energy gradient and the bed slope are equal. The full dynamic wave model uses all the terms in the Saint–Venant equation to simulate unsteady flows. Besides, given the historical records of the past floods and based on the flow continuity equation, the Att-Kin and Muskingum hydrological models deal with flood routing operations. This study describes the principles of Saint–Venant equations and numerical models of dynamic and kinematic-waves, as well as Att-Kin and Muskingum models, the results of which are compared. For this purpose, the Mehrian River range was used. The maximum flood discharge, the maximum area of the river flood plain, and the maximum flood flow width were estimated by presenting a new mathematical relation. The results showed that the MIKE 11 dynamic wave model yields better results than other models by solving partial differential equations. Moreover, among the hydrological methods, the mathematical flood routing and zoning indicate the closeness of Muskingum hydrological results using the least-squares model and the least error with the numerical values of the software for the observed flood.