Congested shallow water model: floating object

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 are interested in the floating body problem on a large space scale. We focus on objects floating freely in the water such as icebergs or wave energy converters. The formulation of the fluid-solid interaction using the congested shallow water model for the fluid and Newton's second law of motion for the solid is given and a strong coupling between the two systems is explained. The energy transfer between the solid and the water is focused on since it is of major interest for energy production. A numerical resolution based on the coupling of a finite 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 validate the method and to show the feasibility of more complex cases.

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

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: floating object. 2018. ⟨hal-01871708v1⟩