Geodesic
Congested shallow water model: on floating body
Godlewski, Edwige1; Parisot, Martin1; Sainte-Marie, Jacques1; Wahl, Fabien1
1Sorbonne Université, université Paris-Diderot SPC, CNRS, Inria, laboratoire Jacques-Louis Lions, LJLL, ANGE team, F-75005 Paris, France
The SMAI Journal of computational mathematics, Volume 6 (2020), pp. 227-251

See the original article notice from the Numdam source

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 a 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 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 verify the method and to show the feasibility of extending it to more complex cases.

Published online:
DOI: 10.5802/smai-jcm.67
Classification: 35Q35, 70E15, 74F10, 76B07, 76M12
Keywords: shallow water equations, wave-body interaction, congested model, coupling, entropy satisfying scheme

Godlewski, Edwige  1 ; Parisot, Martin  1 ; Sainte-Marie, Jacques  1 ; Wahl, Fabien  1

1 Sorbonne Université, université Paris-Diderot SPC, CNRS, Inria, laboratoire Jacques-Louis Lions, LJLL, ANGE team, F-75005 Paris, France 
Godlewski, Edwige; Parisot, Martin; Sainte-Marie, Jacques; Wahl, Fabien. Congested shallow water model: on floating body. The SMAI Journal of computational mathematics, Volume 6 (2020), pp. 227-251. doi: 10.5802/smai-jcm.67
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     title = {Congested shallow water model: on floating body},
     journal = {The SMAI Journal of computational mathematics},
     pages = {227--251},
     year = {2020},
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