Existence for an Unsteady Fluid-Structure Interaction Problem

Céline Grandmont; Yvon Maday

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 3, page 609-636
  • ISSN: 0764-583X

Abstract

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We study the well-posedness of an unsteady fluid-structure interaction problem. We consider a viscous incompressible flow, which is modelled by the Navier-Stokes equations. The structure is a collection of rigid moving bodies. The fluid domain depends on time and is defined by the position of the structure, itself resulting from a stress distribution coming from the fluid. The problem is then nonlinear and the equations we deal with are coupled. We prove its local solvability in time through two fixed point procedures.

How to cite

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Grandmont, Céline, and Maday, Yvon. "Existence for an Unsteady Fluid-Structure Interaction Problem." ESAIM: Mathematical Modelling and Numerical Analysis 34.3 (2010): 609-636. <http://eudml.org/doc/197391>.

@article{Grandmont2010,
abstract = { We study the well-posedness of an unsteady fluid-structure interaction problem. We consider a viscous incompressible flow, which is modelled by the Navier-Stokes equations. The structure is a collection of rigid moving bodies. The fluid domain depends on time and is defined by the position of the structure, itself resulting from a stress distribution coming from the fluid. The problem is then nonlinear and the equations we deal with are coupled. We prove its local solvability in time through two fixed point procedures. },
author = {Grandmont, Céline, Maday, Yvon},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Navier-Stokes; fluid structure interaction.; time-dependent domain; coupled equations; fluid-structure interaction; rigid bodies; incompressible Navier-Stokes equations; local solvability in time; Banach fixed point theorem; contraction mapping principle},
language = {eng},
month = {3},
number = {3},
pages = {609-636},
publisher = {EDP Sciences},
title = {Existence for an Unsteady Fluid-Structure Interaction Problem},
url = {http://eudml.org/doc/197391},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Grandmont, Céline
AU - Maday, Yvon
TI - Existence for an Unsteady Fluid-Structure Interaction Problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 3
SP - 609
EP - 636
AB - We study the well-posedness of an unsteady fluid-structure interaction problem. We consider a viscous incompressible flow, which is modelled by the Navier-Stokes equations. The structure is a collection of rigid moving bodies. The fluid domain depends on time and is defined by the position of the structure, itself resulting from a stress distribution coming from the fluid. The problem is then nonlinear and the equations we deal with are coupled. We prove its local solvability in time through two fixed point procedures.
LA - eng
KW - Navier-Stokes; fluid structure interaction.; time-dependent domain; coupled equations; fluid-structure interaction; rigid bodies; incompressible Navier-Stokes equations; local solvability in time; Banach fixed point theorem; contraction mapping principle
UR - http://eudml.org/doc/197391
ER -

References

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Citations in EuDML Documents

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  1. M. Boulakia, S. Guerrero, A regularity result for a solid-fluid system associated to the compressible Navier-Stokes equations
  2. Patricio Cumsille, Takéo Takahashi, Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid
  3. Cornel Marius Murea, Numerical simulation of a pulsatile flow through a flexible channel
  4. Cornel Marius Murea, Numerical simulation of a pulsatile flow through a flexible channel
  5. Jaime H. Ortega, Lionel Rosier, Takéo Takahashi, Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid
  6. Jaime H. Ortega, Lionel Rosier, Takéo Takahashi, Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid
  7. Jaime Ortega, Lionel Rosier, Takéo Takahashi, On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid

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