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Modèles réduits obtenus par la méthode de POD-Galerkin pour les problèmes d'interaction fluide structure

Abstract : This study presents a contribution of reduced order modelling (ROM) for fluid structure interaction (FSI) problems in the context of optimisation and active control by the Proper Orthogonal Decomposition (POD) method. The first remarkable results using the POD method have been achieved in the field of fluid mechanics. The present study illustrates these results on two practical examples on the Burgers equation and a fluid flow at low Reynolds number around a cylinder. For this cases, the Biorthogonal decomposition has also been tested and gave the same results as the POD. The main subject being ROM in FSI, the POD method has also been tested for structural dynamics. The results show that the POD can be used as a ROM tool in this field.

Then, the POD application for fluid structure interaction problem has been studied. The complexity of this subject area resides in the fact that the POD basis is spatial and the domains are moving. The proposed solution consists in using a fixed reference domain containing all the time variant domains in order to compute the POD basis for the global (fluid and solid) velocity field. ThePOSTDOCTORAL APPOINTMENT first solution has been computed by a classical method (ALE for example), and every snapshot has been interpolated from the time variant grid to the reference grid. This snapshots have been used for computing the POD basis.
The last part of the study presents a low order dynamical system using the POD modes for fluid solid rigid interaction problems. A multiphasic formulation has been considered for the construction of a nonlinear low order dynamical system which has been established by the projection of the continuum formulation of the POD basis. This method has been tested on a one dimensional case and three bidimensional examples. The first bidimensional example considers a case where the solid velocity field is predominant, the second a fluid velocity field at a low Reynolds number and the last a high Reynolds number. The results validate the proposed method.
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https://tel.archives-ouvertes.fr/tel-00348432
Contributor : Erwan Liberge <>
Submitted on : Thursday, December 18, 2008 - 10:16:45 PM
Last modification on : Tuesday, October 3, 2017 - 4:34:01 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 4:29:09 PM

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  • HAL Id : tel-00348432, version 1

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Erwan Liberge. Modèles réduits obtenus par la méthode de POD-Galerkin pour les problèmes d'interaction fluide structure. Mécanique [physics.med-ph]. Université de La Rochelle, 2008. Français. ⟨tel-00348432⟩

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