Coupling 1-D and 2-D Models for Simulating Floods: Definition of the Exchange Terms

Abstract

During floods, the flows in the main channel and the floodplain have very different features. Thus, one can optimize the calculation time by using 1-D model for the main channel and 2-D model for the floodplain in which the flow is more complex. One solution to couple a 1-D model and a 2-D model is proposed. The two models are based on explicit finite volume schemes solving shallow water equations. Thus, the exchange terms are fluxes calculated on the edges that limit the 2-D model on the side of the 1-D model. For the 1-D model, these fluxes are lateral inputs, upstream, or downstream boundary conditions depending on the side of the coupling. This coupled model is tested on experiments in compound channels for a uniform flow and for a rapidly varied flow produced by an obstacle set on the floodplain. Numerical results are coherent with measurements. On uniform flow, energy losses due to the turbulence are missing, which provides too low water depths. On rapidly varied flow, the transfer velocity between main channel and floodplain is reduced if during the calculation of the exchange terms, the values of the 2-D variables on both sides of the boundary are not defined properly; moreover, the recirculation length is underestimated if the turbulent viscosity coefficient is not high enough.