Congested shallow water model: on floating body

Edwige Godlewski (1, 2) , Martin Parisot (1, 2) , Jacques Sainte-Marie (1, 2) , Fabien Wahl (1, 2)

1 ANGE - Numerical Analysis, Geophysics and Ecology
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We consider the floating body problem in the vertical plane on a large space scale. More precisely, we are interested in the numerical modeling of body floating freely on the water such as icebergs or wave energy converters. The fluid-solid interaction is formulated using a congested shallow water model for the fluid and Newton's second law of motion for the solid. We make a particular focus on the energy transfer between the solid and the water since it is of major interest for energy production. A numerical approximation based on the coupling of a nite volume scheme for the fluid and a Newmark scheme for the solid is presented. An entropy correction based on an adapted choice of discretization for the coupling terms is made in order to ensure a dissipation law at the discrete level. Simulations are presented to verify the method and to show the feasibility of extending it to more complex cases.

Mots clés: Congested hyperbolic model; Coupling; Wave-body interaction; Shallow water equations; Entropic scheme

Domaines: Analyse numérique [math.NA]; Modélisation et simulation; Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Géophysique [physics.geo-ph]

Edwige Godlewski, Martin Parisot, Jacques Sainte-Marie, Fabien Wahl. Congested shallow water model: on floating body. 2019. ⟨hal-01871708v2⟩