A three-dimensional fluid–structure interaction method for heart valve modelling

Raoul van Loon; Patrick D. Anderson; Frank P.T. Baaijens; Frans N. van de Vosse

doi:10.1016/j.crme.2005.10.008

Fluid–solid interactions: modeling, simulation, bio-mechanical applications

A three-dimensional fluid–structure interaction method for heart valve modelling

Raoul van Loon ¹; Patrick D. Anderson ²; Frank P.T. Baaijens ¹; Frans N. van de Vosse ¹

¹ Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
² Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

Comptes Rendus. Mécanique, Fluid-solid interactions: modeling, simulation, bio-mechanical applications, Volume 333 (2005) no. 12, pp. 856-866.

Abstract
Résumé

A method is presented for modelling fluid–solid interaction with large transformations of a slender solid body. The fluid flow is described by the unsteady Navier–Stokes equation, and the solid deformation is described by an incompressible hyperelastic Neo-Hookean model. Although the fluid and solid mesh are non-conformal with respect to each other, both domains can be coupled using a Lagrange multiplier. Accuracy and robustness are improved by a computationally inexpensive adaptive meshing scheme which is applied to the fluid mesh at the position of the solid interface. To illustrate the applicability of this method, 2D and 3D model problems are presented that are closely related to dynamical heart-valve computations.

Dans cet article, on présente une méthode pour la modélisation numérique de couplages fluide–solide lorsque le solide est un corps mince. L'écoulement est décrit par les équations de Navier–Stokes instationnaires, la déformation du solide l'étant par un modèle du type Neo-Hookien hyper élastique incompressible. Bien que les maillages fluide et solide ne soient pas en conformité, l'un par rapport à d'autres on peut coupler les regions respectives via un multiplicateur de Lagrange. Par rapport à d'autres approches de ce type, on améliore précision et robustesse par l'utilisation d'une méthode de maillage adaptative, peu coûteuse, appliquée au maillage fluide au voisinage de l'interface avec le solide. Pour évaluer les possibilités de la méthode, on l'applique à la résolution de problèmes modèles, bi et tri-dimensionnels, tous étroitement liés à la simulation numé rique du mouvement des valves cardiaques en régîme dynamique.

Published online: 2005-11-17

DOI: 10.1016/j.crme.2005.10.008

Keywords: Computational fluid mechanics, Heart valves, Fictitious domains, Adaptive meshing, Fluid–structure, Lagrange multipliers
Mots-clés : Mécanique des fluides numérique, Valves cardiaques, Domaines fictifs, Maillages adaptatifs, Couplage fluide–structure, Multiplicateurs de Lagrange

Author's affiliations:

Raoul van Loon ¹; Patrick D. Anderson ²; Frank P.T. Baaijens ¹; Frans N. van de Vosse ¹

¹ Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
² Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

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     author = {Raoul van Loon and Patrick D. Anderson and Frank P.T. Baaijens and Frans N. van de Vosse},
     title = {A three-dimensional fluid{\textendash}structure interaction method for heart valve modelling},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {856--866},
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     doi = {10.1016/j.crme.2005.10.008},
     language = {en},
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Raoul van Loon; Patrick D. Anderson; Frank P.T. Baaijens; Frans N. van de Vosse. A three-dimensional fluid–structure interaction method for heart valve modelling. Comptes Rendus. Mécanique, Fluid-solid interactions: modeling, simulation, bio-mechanical applications, Volume 333 (2005) no. 12, pp. 856-866. doi : 10.1016/j.crme.2005.10.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.10.008/

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