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Fluid-structure coupling

We developed last years with Claire Bost, Georges-Henri Cottet and Thomas Milcent a new modeling of fluid-structure interaction based on the level-set method, with applications in biomechanics for the isolated cardiomyocyte contraction and membrane cell dynamics. From the applied mathematics stand point, these problems were fluid-structure interaction problems with co-dimension 1 structure (membrane) or 0 (isolated cadiomyocyte). In the case of membranes, elastic energies could involve curvature. In the myocyte case elasticity of the (anisotropic) body was coupled with a reaction-diffusion equation accounting for calcium dynamics. As these fluid-structure models involved soft elastic media, we found it welcome to look for an Eulerian formulation of the problem. For the membrane case this lead to a Level Set formulation of the immersed boundary method for which we obtained an existence theorem. For the myocyte problem, we wrote elasticity in Eulerian coordinates and the whole coupling problem in a multi-physics setting.

[1] Bost C., Cottet G.-H. and Maitre E. Convergence Analysis of a Penalization Method for the Three-Dimensional Motion of a Rigid Body in an Incompressible Viscous Fluid. SIAM J. Numer. Anal., 48 (4), 1313–1337, 2010.
[2] Maitre E., Milcent T., Cottet G.-H., Raoult A. and Usson Y. Applications of level set methods in computational biophysics. Math. Comput. Model., 49 (11-12), 2161–2169, 2009. Trends in Application of Mathematics to Medicine. http://hal.archives-ouvertes.fr/hal-00177593/fr/
[3] Cottet G.-H., Maitre E. et Milcent T. Eulerian formulation and level set models for incompressible fluid-structure interaction. ESAIM-Math. Model. Numer. Anal., 42 (3), 471–492, 2008.
[4] Cottet G.-H., Maitre E. and Milcent T. New methods in fluid-structure coupling with application to biomechanics. Proc. Appl. Math. Mech., 7 (1), 1140301–1140302, 2007. Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007.
[5] Cottet G.-H. and Maitre E. A level set method for fluid-structure interactions with immersed surfaces. Math. Models Meth. Appl. Sci., 16 (3), 415–438, 2006.
[6] Cottet G.-H. and Maitre E. A level-set formulation of immersed boundary methods for fluid-structure interaction problems. C. R. Math., 338 (7), 581–586, 2004.

Claire Bost and Thomas Milcent defended their thesis in 2008 and 2009 on that topic:
[1] Bost Claire. Méthodes Level-Set et pénalisation pour le calcul d'interactions fluide-structure. Thèse de doctorat, Université Joseph Fourier. octobre 2008. (HAL)
[2] Milcent Thomas. Une approche eulérienne du couplage fluide-structure, analyse mathématique et applications en biomécanique. Thèse de doctorat, Université Joseph Fourier. mai 2009. (HAL)


Tank-treading motion of a vesicle in a shear flow

Tumbling motion of a vesicle in a shear flow

Contraction d'un cardiomyocyte

Isosurfaces de vorticité lors de la relaxation d'une membrane élastique
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research.txt · Last modified: 2010/12/28 11:29 by maitre