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DGFEM for dynamical systems describing interaction of compressible fluid and structures. (English) Zbl 1290.65089
Summary: The paper is concerned with the numerical solution of flow-induced vibrations of elastic structures. The dependence on time of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the compressible Navier-Stokes equations. The deformation of the elastic body, caused by aeroelastic forces, is described by the linear dynamical elasticity equations. These two systems are coupled by transmission conditions. The flow problem is discretized by the discontinuous Galerkin finite element method (DGFEM) in space and by the backward difference formula (BDF) in time. The structural problem is discretized by conforming finite elements and the Newmark method. The fluid-structure interaction is realized via weak or strong coupling algorithms. The developed technique is tested by numerical experiments and applied to the simulation of vibrations of vocal folds during phonation onset.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D05 Navier-Stokes equations for incompressible viscous fluids
76M10 Finite element methods applied to problems in fluid mechanics
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[1] Badia, S.; Codina, R., On some fluid-structure iterative algorithms using pressure segregation methods. application to aeroelasticity, Internat. J. Numer. Methods Engrg., 72, 46-71, (2007) · Zbl 1194.74361
[2] Sváček, P.; Feistauer, M.; Horáček, J., Numerical simulation of flow induced airfoil vibrations with large amplitudes, J. Fluids Struct., 23, 391-411, (2007)
[3] Titze, I. R., Principles of voice production, (2000), National Centre for Voice and Speech Iowa City
[4] Alipour, F.; Brücker, Ch.; Cook, D. D.; Gömmel, A.; Kaltenbacher, M.; Mattheus, W.; Mongeau, L.; Nauman, E.; Schwarze, R.; Tokuda, I.; Zörner, S., Mathematical models and numerical schemes for the simulation of human phonation, Curr. Bioinform., 6, 323-343, (2011)
[5] Horáček, J.; Šidlof, P.; Švec, J. G., Numerical simulation of self-oscillations of human vocal folds with Hertz model of impact forces, J. Fluids Struct., 20, 853-869, (2005)
[6] F. Alipour, I.R. Titze, Combined simulation of two-dimensional airflow and vocal fold vibration, in: P. J. Davis and N. H. Fletcher (Eds.), Vocal Fold Physiology, Controlling Complexity and Chaos, San Diego, 1996.
[7] De Vries, M. P.; Schutte, H. K.; Veldman, A. E.P.; Verkerke, G. J., Glottal flow through a two-mass model: comparison of Navier-Stokes solutions with simplified models, J. Acoust. Soc. Am., 111, 4, 1847-1853, (2002)
[8] Titze, I. R., The myoelastic aerodynamic theory of phonation, (2006), National Centre for Voice and Speech, Denver Iowa City
[9] Punčochářová-Pořízková, P.; Kozel, K.; Horáček, J., Simulation of unsteady compressible flow in a channel with vibrating walls—influence of the frequency, Comput. & Fluids, 46, 404-410, (2011) · Zbl 1431.76019
[10] Horáček, J.; Švec, J. G., Aeroelastic model of vocal-fold-shaped vibrating element for studying the phonation threshold, J. Fluids Struct., 16, 931-955, (2002)
[11] Zhang, Z.; Neubauer, J.; Berry, D. A., Physical mechanisms of phonation onset: a linear stability analysis of an aeroelastic continuum model of phonation, J. Acoust. Soc. Am., 122, 2279-2295, (2007)
[12] Nomura, T.; Hughes, T. J.R., An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body, Comput. Methods Appl. Mech. Engrg., 95, 115-138, (1992) · Zbl 0756.76047
[13] Feistauer, M.; Horáček, J.; Kučera, V.; Prokopová, J., On numerical solution of compressible flow in time-dependent domains, Math. Bohem., 137, 1-16, (2011) · Zbl 1249.65196
[14] Feistauer, M.; Felcman, J.; Straškraba, I., Mathematical and computational methods for compressible flow, (2003), Clarendon Press Oxford · Zbl 1028.76001
[15] Feistauer, M.; Kučera, V., On a robust discontinuous Galerkin technique for the solution of compressible flow, J. Comput. Phys., 224, 208-221, (2007) · Zbl 1114.76042
[16] Curnier, A., Computational methods in solid mechanics, (1994), Kluwer Academic Publishing Group Dordrecht · Zbl 0815.73003
[17] Horáček, J.; Šidlof, P.; Uruba, V.; Veselý, J.; Radolf, V.; Bula, V., Coherent structures in the flow inside a model of human vocal tract with self-oscillating vocal folds, Acta Tech., 55, 327-343, (2010)
[18] Horáček, J.; Uruba, V.; Radolf, V.; Veselý, J.; Bula, V., Airflow visualization in a model of human glottis near the self-oscillating vocal folds model, Appl. Comput. Mech., 5, 21-28, (2011)
[19] Luo, H.; Mittal, R.; Zheng, X.; Bielamowicz, S. A.; Walsh, R. J.; Hahn, J. K., An immersed-boundary method for flow-structure interaction in biological systems with application to phonation, J. Comput. Phys., 227, 9303-9332, (2008) · Zbl 1148.74048
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