Bathymetry reconstruction via a time-dependent intrinsic shallow water model

In this thesis, we firstly give a presentation of the state of the art of the bathymetry reconstruction problem. Secondly we introduce, in a geometrical setting, the Shallow water model, known for its many applications (dynamics of the athmosphere, geophysical phenomena and more). Furthermore, we use the SW model to derive a novel intrinsic model for the bathymetry reconstruction. More specifically, we find a second order approximation of the Navier-Stokes equations based on the SW model. Finally, employing the Discontinuous Galerkin method, we perform the first steps towards the experimental validation of our model.