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Congested shallow water model: on floating body. (English) Zbl 1464.35223

Summary: 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
70E15 Free motion of a rigid body
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76B07 Free-surface potential flows for incompressible inviscid fluids
76M12 Finite volume methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
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