A simplified dynamic model for flood routing in rectangular channels

Abstract

Abstract A new form of the momentum equation has been derived in order to solve the Saint Venant's equations for flood routing in rectangular open channels with constant width. In this new formulation, the momentum equation transforms to a partial differential equation which has two parameters related to cross-sectional area and discharge of the channel. This simplified dynamic model has been solved by using an explicit finite difference scheme in which the operator is in the form of a tiling diagram. In computation procedure, after computing the discharge from the momentum equation, the cross-sectional area will be obtained from the continuity equation for a given point of the channel. The numerical algorithm used in the model is a simple one of a cascade type. The results are compared with the solution of general dynamic model which was selected from the literature. The comparison shows that there is a good agreement between the results of the simplified dynamic model and those of the general dynamic model. However the simplified model is more easy to formulate and simple to compute than that one. In addition, the solutions of the simplified dynamic method for a flood routing problem are compared with the solutions of kinematic method.