Comptes Rendus
no. 11-12
Variational discretizations for the dynamics of fluid-conveying flexible tubes
[Discrétisations variationnelles pour l'étude de la dynamique de tubes flexibles avec écoulement interne]
François Gay-Balmaz1  ; Vakhtang Putkaradze2
1 LMD/IPSL, CNRS, École normale supérieure, PSL Research University, École polytechnique, Université Paris-Saclay, Sorbonne Universités, UPMC Université Paris-6, 24, rue Lhomond, 75005 Paris, France
2 Department of Mathematical and Statistical Sciences, Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 2G1 Canada
Comptes Rendus. Mécanique, Volume 344 (2016) no. 11-12, pp. 769-775.

Nous proposons une approche variationnelle pour la discrétisation d'interactions fluide–structure, en nous focalisant sur la dynamique de tubes élastiques avec écoulement interne. Notre approche est basée sur une discrétisation des trajectoires inverses du fluide et une discrétisation de type groupe de Lie des variables du tube élastique, couplée à une discrétisation appropriée de la contrainte de préservation du volume de fluide. Notre approche permet le développement de schémas numériques géométriques pour la dynamique des tubes souples avec écoulement interne, qui préservent plusieurs propriétés géométriques intrinsèques du système continu, telles que les symétries et la symplecticité. De plus, notre approche peut être utilisée pour produire des modèles simplifiés et géométriquement consistants, appropriés pour des études analytiques et numériques plus approfondies de ce système.

We derive a variational approach for discretizing fluid–structure interactions, with a particular focus on the dynamics of fluid-conveying elastic tubes. Our method is based on a discretization of the fluid's back-to-labels map and a Lie group discretization of the tube's variables, coupled with an appropriately formulated discrete version of the fluid conservation law. This approach allows the development of geometric numerical schemes for the dynamics of fluid-conveying collapsible tubes, which preserve several intrinsic geometric properties of the continuous system, such as symmetries and symplecticity. In addition, our approach can also be used to derive simplified, but geometrically consistent, low-component models for further analytical and numerical analysis of the system.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2016.08.004
Keywords: Variational integrators, Fluid–structure interaction, Fluid-conveying tubes
Mot clés : Intégrateurs variationnels, Interaction fluide–structure, Tubes avec écoulement interne
François Gay-Balmaz 1 ; Vakhtang Putkaradze 2

1 LMD/IPSL, CNRS, École normale supérieure, PSL Research University, École polytechnique, Université Paris-Saclay, Sorbonne Universités, UPMC Université Paris-6, 24, rue Lhomond, 75005 Paris, France
2 Department of Mathematical and Statistical Sciences, Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 2G1 Canada 
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François Gay-Balmaz; Vakhtang Putkaradze. Variational discretizations for the dynamics of fluid-conveying flexible tubes. Comptes Rendus. Mécanique, Volume 344 (2016) no. 11-12, pp. 769-775. doi : 10.1016/j.crme.2016.08.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.08.004/

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