Modeling and analysis of interactions between free surface flows and floating structures

Fabien Wahl 1
1 ANGE - Numerical Analysis, Geophysics and Ecology
Inria de Paris, LJLL - Laboratoire Jacques-Louis Lions
Abstract : This thesis is about the modeling and the numerical approximation of flows in the presence of a structure at the surface. We consider the floating body problem on a large space scale. It is motivated by applications for geophysical phenomena such as flows under the ice floe and renewable energy production using wave energy converters. We derive a shallow water model with a supplementary congestion constraint. The congestion constraint is a challenging problem for the numerical approximation of hyperbolic equations. Thus we propose a unified model based on a pseudo-compressible relaxation for the resolution. We identify the mandatory properties for the numerical scheme and describe the adaptation of a numerical scheme based on a finite volume method. The well-balanced property and the dissipation of mechanical energy are ensured under a non-restrictive condition on the time step. To take into account freely floating objects, we introduce a coupling between the congested shallow water model and the equations given by Newton's second law of motion and focus on the energy of the coupled system. Indeed, the latter is of major interest for energy production. A Newmark scheme is used to solve the solid dynamics and coupled to the fluid scheme. We propose an entropy correction based on an adapted choice of discretization for the coupling terms in order to ensure a dissipation law at the discrete level. A validation is established in the one dimensional case using stationary and non-stationary analytical solutions.
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Submitted on : Friday, December 14, 2018 - 3:57:00 PM
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Fabien Wahl. Modeling and analysis of interactions between free surface flows and floating structures. Mathematics [math]. Sorbonne Université, 2018. English. ⟨tel-01955798⟩

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