We address the problem of coupling 1D St-Venant equations (Shallow Water) with 2D ones, as applied to floodplain flows (river hydraulics). Continuous coupling conditions are derived, while numerical coupling is done using optimal control processes. In a variationnal data assimilation context, this approach allows to couple both models and assimilate data simultaneously. Two different versions o...

Continental River Dynamics (CRD) is herein defined as modelling the flow dynamics in all channels of a continental-scale river basin using the physics-based Saint-Venant equations. At the boundary of hydraulics and hydrology, CRD requires significant collaborative efforts to make new progress. Six constraints and seven challenges are identified in the areas of dynamics, dimensionality, resoluti...

We present a splitting method for the one-dimensional Saint-Venant-Exner equations used describing bed evolution in shallow water systems. adapt flux vector approach of Toro and Vazquez-Cend\`on identify one subsystem conservative (advection system) non-conservative (pressure system), both having very simple eigenstructure compared to full system. The final numerical scheme is constructed using...