On finite element approximation of incompressible fluid flow in computational domain with vibrating walls: mathematical models for treatment of channel closing
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Abstract
In this paper a simplified mathematical model of a voice production problem is considered. Here we focus on modelling of the glottis closure, which is an important part of phonation process. A simplified vocal fold model describing the vocal fold vibrations with two degrees of freedom is considered and coupled with a simplified model of the fluid flow described by the incompressible Navier-Stokes equations. The vocal fold vibrations cause a deformation of the fluid computational domain which is treated with the aid the Arbitrary Lagrangian-Eulerian method. The vibrations can possible lead to an appearance of the vocal folds contact. This situation is treated with the aid of a combination of inlet boundary conditions, a fictitious porous media approach and the Hertz impact forces. Numerical method is based on the stabilized finite element method. Numerical results are presented.
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Sváček, P.
(2020).
On finite element approximation of incompressible fluid flow in computational domain with vibrating walls: mathematical models for treatment of channel closing.
Proceedings Of The Conference Algoritmy, , 71 - 80.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1556/820
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References
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[2] J. Horáček, P. Šidlof, and J. G. Švec. Numerical simulation of self-oscillations of human vocal folds with Hertz model of impact forces. Journal of Fluids and Structures, 20(6):853–869, 2005.
[3] K. Ishizaka and J. L. Flanagan. Synthesis of voiced sounds from a two-mass model of the vocal coords. The Bell System Technical Journal, 51:1233–1268, 1972.
[4] T. Nomura and T. J. R. Hughes. An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body. Computer Methods in Applied Mechanics and Engineering, 95:115–138, 1992.
[5] P. Sváček and J. Horáček. Numerical simulation of glottal flow in interaction with self oscillating vocal folds: comparison of finite element approximation with a simplified model. Communications in Computational Physics, 12(3):789–806, 2012.
[6] I. R. Titze. The Myoelastic Aerodynamic Theory of Phonation. National Center for Voice and Speech, U.S.A., 2006.
[7] Z. Yang and D. J. Mavriplis. 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.