Congested Shallow Water model, floating structure modeling

The floating body problem on a large space scale is considered. It is motivated by applications for geophysical phenomena such as flows under the ice floe or in sewers, floating icebergs and renewable energy production using wave energy converters. A shallow water model with a supplementary congestion constraint is derived from the Navier-Stokes equations. The congestion constraint is a challenging problem for the numerical approximation of hyperbolic equations. The resolution proposed is based on a pseudo-compressible relaxation of the constraint. The energy transfer between the fluid and the solid is focused on since it is of major interest for energy production. We proof the dissipation of the mechanical energy at the discret level for the fluid-structure interaction. We perform several numerical validation to illustrate our results.