Hydrodynamical modelling and multidimensional approximation of estuarian river flows

We propose a new approach for deriving hydrodynamical models, within the framework of mixed variational formulations. We thus obtain a 2D-horizontal model, as well as a 2D-vertical one and a 1D model taking into account the geometry of the river. We briefly study here the 2D-vertical and the 1D models and we propose (after time discretization) low-order conforming finite element approximations. All the variational problems are well-posed. We justify next a posteriori estimators between the models, which allow us to couple them. Numerical tests, achieved with a realistic bathymetry, are next presented.