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

• Main Author: Wahl, Fabien
• Other Authors: Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université, Jacques Sainte-Marie, Edwige Godlewski
• Format: Doctoral or Postdoctoral Thesis
• Language: French
• Published: HAL CCSD 2018
• Subjects: Shallow water equations; Congested hyperbolic model; Unilateral constraint; Équations de Saint-Venant; Modèle hyperbolique congestionné; Contrainte unilatérale; Schéma well-balanced; Schéma entropique; Schéma bas-Froude; [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]; [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation; [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]; [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]; banquise
• Online Access: https://theses.hal.science/tel-01955798; https://theses.hal.science/tel-01955798v2/document; https://theses.hal.science/tel-01955798v2/file/WAHL_Fabien_these_2018.pdf

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. Cette thèse traite de la modélisation et de la résolution numérique d'écoulements en présence d'une structure à la surface. On considère la problématique d'un objet flottant sur un grand domaine. Les écoulements sous la banquise et la production d'énergie renouvelable grâce à des bouées sont des applications potentielles de ce travail. Nous dérivons un modèle de type Saint-Venant avec une contrainte de congestion supplémentaire. La contrainte de congestion est un défi pour la résolution numérique d'équations ...