Analysis of a simplified model of rigid structure floating in a viscous fluid
SAN MARTIN, Jorge
Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago] [CMM]
Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago] [CMM]
TAKAHASHI, Takéo
Institut Élie Cartan de Lorraine [IECL]
Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization [SPHINX]
Voir plus >
Institut Élie Cartan de Lorraine [IECL]
Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization [SPHINX]
SAN MARTIN, Jorge
Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago] [CMM]
Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago] [CMM]
TAKAHASHI, Takéo
Institut Élie Cartan de Lorraine [IECL]
Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization [SPHINX]
< Réduire
Institut Élie Cartan de Lorraine [IECL]
Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization [SPHINX]
Langue
en
Article de revue
Ce document a été publié dans
Journal of Nonlinear Science. 2019, vol. 29, n° 5, p. 1975–2020
Springer Verlag
Résumé en anglais
We study the interaction of surface water waves with a floating solid constraint to move only in the vertical direction. The first novelty we bring in is that we propose a new model for this interaction, taking into ...Lire la suite >
We study the interaction of surface water waves with a floating solid constraint to move only in the vertical direction. The first novelty we bring in is that we propose a new model for this interaction, taking into consideration the viscosity of the fluid. This is done supposing that the flow obeys a shallow water regime (modeled by the viscous Saint-Venant equations in one space dimension) and using a Hamiltonian formalism. Another contribution of this work is establishing the well-posedness of the obtained PDEs/ODEs system in function spaces similar to the standard ones for strong solutions of viscous shallow water equations. Our well-posedness results are local in time for every initial data and global in time if the initial data are close (in appropriate norms) to an equilibrium state. Moreover, we show that the linearization of our system around an equilibrium state can be described, at least for some initial data, by an integro-fractional differential equation related to the classical Cummins equation and which reduces to the Cummins equation when the viscosity vanishes and the fluid is supposed to fill the whole space. Finally, we describe some numerical tests, performed on the original nonlinear system, which illustrate the return to equilibrium and the influence of the viscosity coefficient.< Réduire
Mots clés en anglais
Viscous shallow water equations
floating structure
strong solutions
fluid-structure interaction
return to equilibrium
Project ANR
Systèmes interconnectés de dimension infinie pour les milieux hétérogènes - ANR-16-CE92-0028
Origine
Importé de halUnités de recherche