Review on Fluid Structure Interaction Solution Method for Biomechanical Application

Abstract:

Fluid-Structure Interaction engages with complex geometry especially in biomechanical problem. In order to solve critical case studies such as cardiovascular diseases, we need the structure to be flexible and interact with the surrounding fluids. Thus, to simulate such systems, we have to consider both fluid and structure two-way interactions. An extra attention is needed to develop FSI algorithm in biomechanic problem, namely the algorithm to solve the governing equations, the coupling between the fluid and structural parameter and finally the algorithm for solving the grid connectivity. In this article, we will review essential works that have been done in FSI for biomechanic. Works on Navier–Stokes equations as the basis of the fluid solver and the equation of motion together with the finite element methods for the structure solver are thoroughly discussed. Important issues on the interface between structure and fluid solvers, discretised via Arbitrary Lagrangian–Eulerian grid are also pointed out. The aim is to provide a crystal clear understanding on how to develop an efficient algorithm to solve biomechanical Fluid-Structure Interaction problems in a matrix based programming platform.

• Periodical: Applied Mechanics and Materials (Volume 660)
• Pages: 927-931
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.660.927
• Online since: October 2014
• Authors: Nazri Huzaimi bin Zakaria, Mohd Zamani Ngali, Ahmad Rivai
• Keywords: ALE, Biomechanical, Fluid Structure Interaction (FSI), Navier-Stokes

References

[1] R. van Loon, P.D. Anderson, F.N. van de Vosse. A fluid–structure interaction method with solid-rigid contact for heart valve dynamics. Journal of Computational Physics 217 (2006) 806–823.

DOI: 10.1016/j.jcp.2006.01.032

[2] Gene Hou, Jin Wang, and Anita Layton. Numerical Methods for Fluid-Structure Interaction- A Review. Communications in Computational Physics (2012), Vol. 12, No. 2, pp.337-377. doi: 10. 4208/cicp. 291210. 290411s.

DOI: 10.4208/cicp.291210.290411s

[3] J. Vierendeels, K. Dumont, P.R. Verdonck. A partitioned strongly coupled fluid-structure interaction method to model heart valve dynamics. Journal of Computational and Applied Mathematics 215 (2008) 602 – 609.

DOI: 10.1016/j.cam.2006.04.067

[4] Hubner, B., Walhorn, E. and Dinkler, D. (2004). A monolithic approach to fluid-structure interaction using space-time finite elements, Computer Methods in Applied Mechanics and Engineering, Vol. 193, pp.2087-2104.

DOI: 10.1016/j.cma.2004.01.024

[5] Ryzhakov, P. B., Rossi, R., Idelsohn, S. R. and O˜nate, E., (2010). A monolithic Lagrangian approach for fluid-structure interaction problems, Computational Mechanics, Vol. 46, pp.883-899.

DOI: 10.1007/s00466-010-0522-0

[6] Jean Donea and Antonio Huerta (2003). Finite Elements Methods for Flow Problems. 1st ed. England: Wiley. pp.4-5.

[7] Hirt, C., Amsden, A., and Cook, J. An Arbitrary Lagrangian Eulerian Finite element method for all flow speeds. Journal of Computational Physics 14 (1974), 227-253.

DOI: 10.1016/0021-9991(74)90051-5

[8] Donea, J., Fasoli-Stella, P., and Giuliani, S. Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems. In Transaction of the 4th Conference (San Francisco, 1977), p. Paper B1/2.

[9] Baaijens, F. An U-ALE formulation of 3-D unsteady viscoelastic flow. International Journal of Numerical Methods in Engineering 36(7) (1993), 1115-1143.

DOI: 10.1002/nme.1620360704

[10] Nomura, T., and Hughes, T. An Arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body. Computer Methods in Applied Mechanics and Engineering 95 (1992), 115-138.

DOI: 10.1016/0045-7825(92)90085-x

[11] Donea, J., S. Giuliani, J. Halleux, An arbitrary Lagrangian–Eulerian finite element method for transient dynamic fluid–structure interactions, Computer Methods in Applied Mechanics and Engineering 33 (1–3) (1982) 689–723.

DOI: 10.1016/0045-7825(82)90128-1

[12] Peskin, C.S. Flow patterns around heart valves: a numerical method, Journal of Computational Physics 10 (1972) 252–271.

DOI: 10.1016/0021-9991(72)90065-4

[13] Borazjani, I., Liang Ge, Fotis Sotiropoulos. Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. Journal of Computational Physics. 227 (2008), 7587-7620.

DOI: 10.1016/j.jcp.2008.04.028

[14] 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. C. R. Mecanique 333 (2005) 856–866.

DOI: 10.1016/j.crme.2005.10.008

[15] Singiresu S. Rao (2005). Mechanical Vibrations. 4th ed. Malaysia: Pearson Education & Prentice-Hall, Inc. pp.17-18, 109-112.