Comptes Rendus
Fluid–solid interactions: modeling, simulation, bio-mechanical applications
A three-dimensional fluid–structure interaction method for heart valve modelling
Comptes Rendus. Mécanique, Volume 333 (2005) no. 12, pp. 856-866.

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:
DOI: 10.1016/j.crme.2005.10.008
Keywords: Computational fluid mechanics, Heart valves, Fictitious domains, Adaptive meshing, Fluid–structure, Lagrange multipliers
Mot clés : Mécanique des fluides numérique, Valves cardiaques, Domaines fictifs, Maillages adaptatifs, Couplage fluide–structure, Multiplicateurs de Lagrange

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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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, 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/

[1] C.S. Peskin Flow patterns around heart valves: a numerical method, J. Comput. Phys., Volume 10 (1972), pp. 252-271

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

[3] C.S. Peskin; D.M. McQueen A three-dimensional computational method for blood flow in the heart I. Immersed elastic fibers in a viscous incompressible fluid. The immersed boundary method, J. Comput. Phys., Volume 81 (1989), pp. 372-405

[4] D.M. McQueen; C.S. Peskin Shared-memory parallel vector implementation of the immersed boundary method for the computation of blood flow in the beating mamalian heart, J. Supercomp., Volume 11 (1997), pp. 213-236

[5] V.B. Makhijani; H.Q. Yang; P.J. Dionne; M.J. Thubrikar Three-dimensional coupled fluid–structure simulation of pericardial bioprosthetic aortic valve functioning, ASAIO J., Volume 43 (1997) no. 5, pp. 387-392

[6] C.W. Hirt; A.A. Amsden; J.L. Cook An arbitrary Lagrangian–Eulerian computing method for all speeds, J. Comput. Phys., Volume 14 (1974), pp. 227-253

[7] T.J.R. Hughes; W.K. Liu; T. Zimmerman Lagrangian–Eulerian finite element formulation for incompressible viscous flow, Comput. Methods Appl. Mech. Engrg., Volume 29 (1981), pp. 329-349

[8] J. Donea; S. Giuliani; J.P. Halleux An arbitrary Lagrangian–Eulerian finite element method for transient dynamic fluid–structure interactions, Comput. Methods Appl. Mech. Engrg., Volume 33 (1982), pp. 689-723

[9] M.A. Nicosia; R.P. Cochran; D.R. Einstein; C.J. Rutland; K.S. Kunzelman A coupled fluid–structure finite element model of the aortic valve and root, J. Heart Valve Disease, Volume 12 (2003), pp. 781-789

[10] J. de Hart; G.W.M. Peters; P.J.G. Schreurs; F.P.T. Baaijens A three-dimensional computational analysis of fluid–structure interaction in the aortic valve, J. Biomech., Volume 36 (2003) no. 1, pp. 103-112

[11] J. de Hart; G.W.M. Peters; P.J.G. Schreurs; F.P.T. Baaijens A computational fluid–structure interaction analysis of a fiber-reinforced stentless aortic valve, J. Biomech., Volume 36 (2003) no. 5, pp. 699-712

[12] J. de Hart; G.W.M. Peters; P.J.G. Schreurs; F.P.T. Baaijens Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole, J. Biomech., Volume 37 (2004), pp. 303-311

[13] R. Glowinski; T.-W. Pan; J. Périaux A Lagrange multiplier/fictitious domain method for the numerical simulation of incompressible viscous flow around moving rigid bodies: (I) case where the rigid body motions are known a priori, C. R. Acad. Sci. Paris, Volume 25 (1997) no. 5, pp. 361-369

[14] R. Glowinski Finite element methods for incompressible viscous flow (P.G. Ciarlet; J.L. Lions, eds.), Handbook of Numerical Analysis, vol. IX, North-Holland, Amsterdam, 2003 (3-1176)

[15] F. Bertrand; P.A. Tanguy; F. Thibault A three-dimensional fictitious domain method for incompressible fluids flow problems, Int. J. Numer. Methods Fluids, Volume 25 (1997) no. 6, pp. 719-736

[16] F.P.T. Baaijens A fictitious domain/mortar element method for fluid–structure interaction, Int. J. Numer. Methods Fluids, Volume 35 (2001) no. 7, pp. 743-761

[17] N.A. Patankar; P. Singh; D.D. Joseph; R. Glowinski; T.W. Pan A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow, Volume 26 (2000) no. 9, pp. 1509-1524

[18] J.M.A. Stijnen; J. de Hart; P.H.M. Bovendeerd; F.N. van de Vosse Evaluation of a fictitious domain method for predicting dynamic response of mechanical heart valves, J. Fluid Struct., Volume 19 (2004), pp. 835-850

[19] R. van Loon; P.D. Anderson; J. de Hart; F.P.T. Baaijens A combined fictitious domain/adaptive meshing method for fluid–structure interaction in heart valves, Int. J. Numer. Methods Fluids, Volume 46 (2004), pp. 533-544

[20] V. Girault; P.A. Raviart Finite Element Approximation of the Navier–Stokes Equations, Lecture Notes in Math., vol. 749, Springer-Verlag, New York, 1979

[21] F. Brezzi; M. Fortin Mixed and Hybrid Finite Element Methods, Springer-Verlag, 1991

[22] G. Segal SEPRAN Introduction, User's Manual, Programmer's Guide and Standard Problems, Ingenieursbureau SEPRA, Leidschendam, 2003

[23] HSL(2002), A collection of Fortran codes for large scale scientific computation, http://www.numerical.rl.ac.uk/hsl

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