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Numerical Simulation of Glottal Flow in Interaction with Self Oscillating Vocal Folds: Comparison of Finite Element Approximation with a Simplified Model

Published online by Cambridge University Press:  20 August 2015

P. Sváček  and
J. Horáček
P. Sváček*
Affiliation:
Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University in Prague, Karlovo nám. 13, Praha 2, 121 35, Czech Republic
J. Horáček*
Affiliation:
Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 5, Praha 8, Czech Republic
*
Corresponding author.Email:Petr.@[email protected]
Email:[email protected]
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Abstract

In this paper the numerical method for solution of an aeroelastic model describing the interactions of air flow with vocal folds is described. The flow is modelled by the incompressible Navier-Stokes equations spatially discretized with the aid of the stabilized finite element method. The motion of the computational domain is treated with the aid of the Arbitrary Lagrangian Eulerian method. The structure dynamics is replaced by a mechanically equivalent system with the two degrees of freedom governed by a system of ordinary differential equations and discretized in time with the aid of an implicit multistep method and strongly coupled with the flow model. The influence of inlet/outlet boundary conditions is studied and the numerical analysis is performed and compared to the related results from literature.

Keywords

74F1065Z0576D05Finite element methodarbitrary Lagrangian-Eulerian methodbiomechanics of voice production
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 3 , September 2012 , pp. 789 - 806
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Alku, P., Horáček, J., Airas, M., Griffond-Boitier, F., and Laukkanen, A. M.. Performance of glottal inverse filtering as tested by aeroelastic modelling of phonation and FE modelling of vocal tract. Acta Acustica united with Acustica, 92(5):717724, 2006.Google Scholar
[2]Baken, R. J. and Orlikoff, R. F.. Clinical Measurement of Speech and Voice. Singular Publishing Group Inc., San Diego, California, 2nd edition, 2000.Google Scholar
[3]Bathe, K. J., editor. Computational Fluid and Solid Mechanics 2007. Elsevier, 2007.Google Scholar
[4]Berry, D. A., Herzel, H., Titze, R., and Krischer, K.. Interpretation of biomechanical simulations of normal and chaotic vocal fold oscillations with empirical eigenfunctions. Journal of the Acoustical Society of America, 95(6):35953604, 1994.Google Scholar
[5]Bruneau, Ch.-H. and Fabrie, P.. Effective downstream boundary conditions for incompressible navierstokes equations. International Journal for Numerical Methods in Fluids, 19(8):693705, 1994.Google Scholar
[6]Codina, R.. Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods. Computational Method in Applied Mechanical Engineering, 190:15791599, 2000.CrossRefGoogle Scholar
[7]Davis, T. A. and Duff, I. S.. A combined unifrontal/multifrontal method for unsymmetric sparse matrices. ACM Transactions on Mathematical Software, 25:119, 1999.Google Scholar
[8]de Vries, M. P., Shutte, H. K., Veldman, A. E. P., and Verkerke, G.J.. Glottal flow through a two-mass model: Comparison of Navier-Stokes solutions with simplified models. Journal of Acoust. Soc. Am., 111(4):18471853, 2002.Google Scholar
[9]Dowell, E. H.. A Modern Course in Aeroelasticity. Kluwer Academic Publishers, Dodrecht, 1995.Google Scholar
[10]Gelhard, T., Lube, G., Olshanskii, M. A., and Starcke, J.-H.. Stabilized finite element schemes with LBB-stable elements for incompressible flows. Journal of Computational and Applied Mathematics, 177:243267, 2005.Google Scholar
[11]Heywood, J. G., Rannacher, R., and Turek, S.. Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Math. Fluids, 22:325352, 1992.Google Scholar
[12]Horáček, J., Laukkanen, A. M., Sidlof, P., Murphy, P., and Svec, J.G.. Comparisonof acceleration and impact stress as possible loading factors in phonation. A computer modeling study. Folia Phoniatrica et Logopaedica, 61(3):137145, 2009.Google Scholar
[13]Horáček, J., Laukkanen, A.M., and Sidlof, P.. Estimation of impact stress using an aeroelastic model of voice production. Logopedics Phoniatrics Vocology, 37:185192, 2007.Google Scholar
[14]Horáček, J., Sidlof, P., and Svec, J. G.. Numerical simulation of self-oscillations of human vocal folds with Hertz model of impact forces. Journal of Fluids and Structures, 20(6):853869, 2005.CrossRefGoogle Scholar
[15]Horáček, J. and Svec, J. G.. Instability boundaries of a vocal fold modelled as a flexibly rigid body vibrating in a channel conveying fluid. AMD, American Society of Mechanical Engineers, Applied Mechanics Division, 253(2):10431054, 2002.Google Scholar
[16]Horáček, J. and Svec, J. G.. Aeroelastic model of vocal-fold-shaped vibrating element for studying the phonation threshold. Journal of Fluids and Structures, 16(7):931955, 2002.Google Scholar
[17]Ishizaka, K. and Flanagan, J. L.. Synthesis of voiced sounds from a two-mass model of the vocal coords. The Bell System Technical Journal, 51:12331268, 1972.Google Scholar
[18]Link, G., Kaltenbacher, M., Breuer, M., and Düllinger, M.. A 2D finite element scheme for fluid-solid-acoustic interactions and its application to human phonation. Computation Methods in Applied Mechanical Engineering, 198:33213334, 2009.Google Scholar
[19]Nomura, T. and Hughes, T. J. R.. An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body. Computer Methods in Applied Mechanics and Engineering, 95:115138, 1992.Google Scholar
[20]Punočhářová, P., Fürst, J., Kozel, K., and Horáč, J.. Numerical simulation of compressible flow with low Mach number through oscillating glottis. In Zolotarev, I. and Horáč, J., editors, Flow Induced Vibrations, Prague, 2008. Institute of Thermomechanics, AS CR.Google Scholar
[21]Sváček, P., Feistauer, M., and Horáč, J.. Numerical simulation of flow induced airfoil vibrations with large amplitudes. Journal of Fluids and Structure, 23(3):391411, 2007.Google Scholar
[22]Titze, I. R.. Physiologic and acoustic differences between male and female voices. Journal of the Acoustical Society of America, 85(4):16991707, 1989.Google Scholar
[23]Yang, Z. and Mavriplis, D. J.. Unstructured dynamic meshes with higher-order time integration schemes for the unsteady Navier-Stokes equations. In 43rd AIAA Aerospace Sciences Meeting, page 13 pp., Reno NV, January 2005. AIAA Paper 2005-1222.Google Scholar