Multidimensional approximation of hydrodynamical models

Hydrodynamical models for river flows are given by the Navier Stokes equations with specific boundary conditions. These models are often of Saint Venant or shallow water type. We present three models derived from the original 3-D model by conforming approaches. These models are 2D-horizontal, 2D-vertical and a 1-D model. The mathematical models induced are well posed and we propose their discretization using finite element methods. Using adequate a posteriori error estimators between these models, we obtain an adaptative multidimensional approximation of river flows. We present numerical tests compared to experimental data.