Congested shallow water model: on floating body
The SMAI Journal of computational mathematics, Volume 6 (2020), pp. 227-251.

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

1 Sorbonne Université, université Paris-Diderot SPC, CNRS, Inria, laboratoire Jacques-Louis Lions, LJLL, ANGE team, F-75005 Paris, France
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author = {Edwige Godlewski and Martin Parisot and Jacques Sainte-Marie and Fabien Wahl},
title = {Congested shallow water model: on floating body},
journal = {The SMAI Journal of computational mathematics},
pages = {227--251},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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Edwige Godlewski; Martin Parisot; Jacques Sainte-Marie; Fabien Wahl. 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. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.67/

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