Skip to main content Accessibility help

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

  • P. Sváček (a1) and J. Horáček (a2)


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.


Corresponding author



Hide All
[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.
[2]Baken, R. J. and Orlikoff, R. F.. Clinical Measurement of Speech and Voice. Singular Publishing Group Inc., San Diego, California, 2nd edition, 2000.
[3]Bathe, K. J., editor. Computational Fluid and Solid Mechanics 2007. Elsevier, 2007.
[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.
[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.
[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.
[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.
[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.
[9]Dowell, E. H.. A Modern Course in Aeroelasticity. Kluwer Academic Publishers, Dodrecht, 1995.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[22]Titze, I. R.. Physiologic and acoustic differences between male and female voices. Journal of the Acoustical Society of America, 85(4):16991707, 1989.
[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.


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

  • P. Sváček (a1) and J. Horáček (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed