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Fluid-Structure Interaction: Modelisation, Analyse, Control, Simulation – IFSMACS

IFSMACS

Fluid-Structure Interaction: Modeling, Analysis, Control and Simulation

Understanding the Fluid-Structure Interaction systems

The aim of this project is to analyze systems composed by structures immersed in a fluid. Studies of such systems can be motivated by many applications (motion of the blood in veins, fish locomotion, design of submarines, etc.) but also by the corresponding challenging mathematical problems. Among the important difficulties inherent to these systems, one can quote nonlinearity, coupling, free-boundaries. We gather several researchers on this subject from Bordeaux, Nancy, Paris and Toulouse and this project will help developing stronger collaborations and will allow many breakthroughs in this field. Our objectives include asymptotic analyses of FSIS, the study of controllability and stabilizability of FSIS, the understanding of locomotion of self-propelled structures and the analyze and development of numerical tools to simulate fluid-structure system.

We have split our work into 3 tasks:
• Asymptotic analysis of fluid-structure interaction systems
• Control and stabilization of fluid-structure interaction systems
• Self-propelled solids into a fluid

The tools used are the standard method for partial differential equations: Galerkin method, semigroup theory, but coupled with technics allowing to reduce to a cylindrical domain: change of variables, penalization, etc.

• Convergence of a fluid-rigid bodies system in the case when the size of the structures goes to 0: case of a bi-dimensional motion and of a solid with the shape of a disk.
• Asymptotic behavior of the Euler system in a perforated domain
• Study of the behavior of a viscous fluid in a high Reynolds flow and in the presence of roughness.
• Study of Navier-Stokes fluid with boundary conditions of type “Coulomb”.
• Stabilization of a system composed by a Navier-Stokes fluid with a structure of type “viscous” beam at its boundary
• Existence and uniqueness of a solutions for the problem of interaction between a compressible fluid modeled by the Navier-Stokes system and an elastic structure whose motion is described by the nonlinear model of Saint-Venant Kirchhoff.
• Self-propelled motion into a fluid modeled by the stationary Navier-Stokes system.

• Convergence of a fluid-rigid bodies system in the case when the size of the structures goes to 0: case of the dimension 3 in space or case of solid with arbitrary shape
• Study of a fluid-structure system with boundary conditions of type “Coulomb” for the fluid.
• Study and stabilization of a system composed by a Navier-Stokes fluid with a structure of type non “viscous” beam at its boundary
• Well-posedness of for the problem of interaction between a viscous incompressible fluid modeled by the Navier-Stokes system and an elastic structure
• Self-propelled motion of rigid bodies with tangential controls

We have obtained 10 publications in international journals.

The aim of this project is to analyze systems composed by structures immersed in a fluid. Studies of such systems can be motivated by many applications
(motion of the blood in veins, fish locomotion, design of submarines, etc.) but also by the corresponding challenging mathematical problems.
Among the important difficulties inherent to these systems, one can quote the nonlinearities, the coupling, the free-boundaries.
We gather several researchers working on this subject from Bordeaux, Nancy, Paris and Toulouse and this project will help developing stronger collaborations and will allow many breakthroughs in this field.
Our objectives include asymptotic analyses of fluid-structure interaction systems (FSIS), the study of controllability and stabilizability of FSIS, the understanding of locomotion of self-propelled structures and the analyze and development of numerical tools to simulate fluid-structure systems.

Project coordination

Takéo Takahashi (Institut National de Recherche en Informatique et en Automatique)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

UPS-IMT Université Toulouse III Paul Sabatier - Institut de Mathématiques de Toulouse -
Inria Paris Rocquencourt Institut National de Recherche en Informatique et en Automatique
INRIA Institut National de Recherche en Informatique et en Automatique
IMB Institut de Mathématiques de Bordeaux

Help of the ANR 352,071 euros
Beginning and duration of the scientific project: September 2015 - 48 Months

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