A level-set formulation of immersed boundary methods for fluid–structure interaction problems

Georges-Henri Cottet; Emmanuel Maitre

doi:10.1016/j.crma.2004.01.023

Numerical Analysis

A level-set formulation of immersed boundary methods for fluid–structure interaction problems

Presented by: Olivier Pironneau

Georges-Henri Cottet ¹; Emmanuel Maitre ¹

¹ Laboratoire LMC-IMAG, Université Joseph Fourier, 38041 Grenoble cedex 9, France

Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 581-586.

Abstract
Résumé

We propose a level set formulation of the immersed boundary method for fluid–structure problems in two and three dimensions. We prove that the resulting model verifies an energy estimate.

On propose dans cette Note une formulation par ensembles de niveau de la méthode de frontière immergée, dans le cadre d'un problème de couplage fluide–structure en dimension deux ou trois. On démontre que le modèle obtenu vérifie une estimation d'énergie.

Received: 2003-11-23
Accepted: 2004-01-27
Published online: 2004-03-17

DOI: 10.1016/j.crma.2004.01.023

Author's affiliations:

Georges-Henri Cottet ¹; Emmanuel Maitre ¹

¹ Laboratoire LMC-IMAG, Université Joseph Fourier, 38041 Grenoble cedex 9, France

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     author = {Georges-Henri Cottet and Emmanuel Maitre},
     title = {A level-set formulation of immersed boundary methods for fluid{\textendash}structure interaction problems},
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Georges-Henri Cottet; Emmanuel Maitre. A level-set formulation of immersed boundary methods for fluid–structure interaction problems. Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 581-586. doi : 10.1016/j.crma.2004.01.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.01.023/

References
Cited by

[1] Y.C. Chang; T.Y. Hou; B. Merriman; S. Osher A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, J. Comp. Phys., Volume 124 (1996), pp. 449-464

[2] G.-H. Cottet, E. Maitre, in preparation

[3] G.-H. Cottet, E. Maitre, Ph. Tracqui, in preparation

[4] S. Osher; R. Fedkiw Level Set Methods and Dynamic Implicit Surfaces, Springer-Verlag, New York, 2002

[5] C.S. Peskin Numerical analysis of blood flow in the heart, J. Comput. Phys., Volume 25 (1977), pp. 220-252

[6] C.S. Peskin The immersed boundary method, Acta Numer., Volume 11 (2002), pp. 479-517

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