Integration of 1D and 2D finite volume schemes for computations of water flow in natural channels

A wide variety of flood simulation models are available nowadays. Some of them use a 1D approach and others a 2D one, but there are also some which allow the performance of integrated 1D–2D simulations. These latter models, which have important advantages in optimizing computational costs, commonly use the 1D approach in river channels and the 2D one in floodplains. The coupling of 1D and 2D flows usually ensures mass conservation and makes use of simplified weir-type or friction slope equations, but neglects momentum transfer between the two domains. This paper presents a fully conservative method for the coupling of 1D and 2D domains to be used in numerical schemes based on finite volumes. The method, based on a discretization of the numerical fluxes which ensures the conservation of mass and momentum, is verified with simple test cases. The proposed scheme is compared with the standard method based on the source term of the equations and is applied to the hydrodynamic characterization of a river-reservoir system situated in the River Ebro in Spain.

► Most available flood simulation models use a1D or a 2D one, but very few an integrated 1D–2D approach.
► Integrated 1D–2D models, usually ensure mass conservation but neglect momentum exchange between domains.
► A new method integrating the 1D and 2D Saint Venant equations (mass and momentum) for finite volumes schemes is presented.
► The momentum exchange between 1D and 2D domains is achieved thanks to an accurate treatment of the numerical fluxes.
► Significant improvements in the flood plain velocity field can be observed when momentum exchange is included.