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A unified formulation for continuum mechanics applied to fluid-structure interaction in flexible tubes. (English) Zbl 1122.74379
Summary: This paper outlines the development of a new procedure for analysing continuum mechanics problems with a particular focus on fluid-structure interaction in flexible tubes. A review of current methods of fluid-structure coupling highlights common limitations of high computational cost and solution instability. It is proposed that these limitations can be overcome by an alternative approach in which both fluid and solid components are solved within a single discretized continuum domain. A single system of momentum and continuity equations is therefore derived that governs both fluids and solids and which are solved with a single mesh using finite volume discretization schemes. The method is validated first by simulating dynamic oscillation of a clamped elastic beam. It is then applied to study the case of interest - wave propagation in highly flexible tubes - in which a predicted wave speed of 8.58 m/s falls within 2% of an approximate analytical solution. The method shows further good agreement with analytical solutions for tubes of increasing rigidity, covering a range of wave speeds from those found in arteries to that in the undisturbed fluid.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S10 Finite volume methods applied to problems in solid mechanics
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[1] Korteweg, Annalen der Physik und Chemie 5 pp 525– (1878)
[2] . Fluid Mechanics. McGraw-Hill: New York, 1979. · Zbl 0471.76001
[3] Young, Philosophical Transactions of the Royal Society of London 98 pp 164– (1808)
[4] Joukowsky, Mémoires de l’Académie Impériale des Sciences de St.-Pétersbourg, 1900, Series 8 9 (1898)
[5] Reuderink, Journal of Biomechanics 22 pp 819– (1989)
[6] Hilbert, Colloquia Mathematica Societatis Janos Bolyai 50 pp 439– (1986)
[7] Steinman, Journal of Biomechanical Engineering–Transactions of the ASME 116 pp 294– (1994)
[8] Perktold, Journal of Biomechanics 28 pp 845– (1995)
[9] Zhao, Proceedings of the Institution of Mechanical Engineers, Part H 212 pp 241– (1998)
[10] Tang, Computers and Structures 72 pp 357– (1999)
[11] Bathe, Journal of Biomechanical Engineering–Transactions of the ASME 121 pp 361– (1999)
[12] Henry, Advances in Bioengineering–American Society of Mechanical Engineers BED26 pp 131– (1993)
[13] Greenshields, Computer Modeling and Simulation in Engineering 4 pp 213– (1999)
[14] Demirdzić, Computer Methods in Applied Mechanics and Engineering 109 pp 331– (1993)
[15] Demirdzić, International Journal for Numerical Methods in Engineering 37 pp 3751– (1994)
[16] Jasak, International Journal for Numerical Methods in Engineering 48 pp 267– (2000)
[17] Chow, International Journal for Numerical Methods in Engineering 35 pp 1849– (1992)
[18] Demirdzić, Computer Methods in Applied Mechanics and Engineering 125 pp 235– (1995)
[19] Bailey, Journal of Computational and Applied Mathematics 103 pp 3– (1999)
[20] Introduction to the Mechanics of a Continuous Medium. Prentice-Hall: Englewood Cliffs, NJ, 1969.
[21] . Computational Methods for Fluid Dynamics. Springer: Berlin, Germany, 1996. · Zbl 0869.76003
[22] Jasak, International Journal for Numerical Methods in Fluids 31 pp 431– (1999)
[23] Issa, Journal of Computational Physics 62 pp 40– (1986)
[24] . A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. AIAA-82-0998, AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference, St. Louis, MO, 1982.
[25] . Applied Iterative Methods. Academic Press: New York, 1981. · Zbl 0459.65014
[26] Weller, Computers in Physics 12 pp 620– (1998)
[27] . Advanced Strength and Applied Elasticity. Prentice-Hall: Englewood Cliffs, NJ, 1994.
[28] . Mechanical Vibrations. Wiley: Chichester, U.K., 1997.
[29] The Fluid Mechanics of Large Blood Vessels. Cambridge University Press: Cambridge, U.K., 1980. · Zbl 0449.76100
[30] Barez, International Journal of Mechanical Sciences 21 pp 223– (1979)
[31] Kellner, 3R International 21 pp 443– (1982)
[32] . Fluid Transients in Systems. Prentice-Hall: Englewood Cliffs, NJ, 1993.
[33] Stuckenbruck, Journal of Fluids Engineering–Transactions of the ASME 107 pp 518– (1985)
[34] Wheel, International Journal for Numerical Methods in Engineering 44 pp 1843– (1999) · Zbl 0935.74075
[35] Finite Element Procedures. Prentice-Hall: Englewood Cliffs, NJ 1997.
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