A multilayer Saint-Venant model: Derivation and numerical validation

We introduce a new variant of the multilayer Saint-Venant system. The classical Saint-Venant system is a well-known approximation of theincompressible Navier-Stokes equations for shallow water flows with free moving boundary. Its efficiency, robustness and low computational cost make itvery commonly used. Nevertheless its range of application is limited and itdoes not allow to access to the vertical profile of the horizontal velocity. Henceand thanks to a precise analysis of the shallow water assumption we proposehere a new approximation of the Navier-Stokes equations which consists in aset of coupled Saint-Venant systems, extends the range of validity and gives aprecise description of the vertical profile of the horizontal velocity while preserving the computational efficiency of the classical Saint-Venant system. Wevalidate the model through some numerical examples.