Abstract
A high order finite-difference method has been developed to model fluid–structure interaction during phonation in the human larynx. The motion of the vocal folds is obtained by solving the elastic equations while the airflow is modeled by solving the compressible Navier–Stokes equations. In this paper, we address the problem of obtaining time-stable solutions for the linear elastic equations.
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References
M.H. Carpenter, D. Gottlieb, and S. Abarbanel. Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes. J. Comput. Phys., 111:220–236, 1994
B. Gustafsson. High order difference methods for time-dependent PDE. Springer, Berlin, 2008
M. Larsson and B. Müller. Numerical simulation of fluid-structure interaction in human phonation: Application. In Proceedings of ENUMATH 2009 Eighth European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, 2009 (to be published by Springer)
M. Larsson and B. Müller. Strictly stable high order difference method for the linear elastic wave equation. Commun. Comput. Phys. (Submitted)
H. Luo, R. Mittal, X. Zheng, S.A. Bielamowicz, R.J. Walsh, and J.K. Hahn. An immersed-boundary method for flow – structure interaction in biological systems with application to phonation. J. Comput. Phys., 227:9303–9332, 2008
K. Mattsson, F. Ham, and G. Iaccarino. Stable boundary treatment for the wave equation on second-order form. J. Sci. Comput., 41:366–383, 2009
B. Müller. High order numerical simulation of aeolian tones. Comput. Fluid, 37(4):450–462, 2008
B. Strand. Summation by parts for finite difference approximations for d/dx. J. Comput. Phys., 110:47–67, 1994
I.R. Titze. Principles of voice production. National Center for Voice and Speech, 2000
Acknowledgements
The authors thank Bjørn Skallerud, Paul Leinan and Victorien Prot at the Department of Structural Engineering, NTNU for valuable discussions on the structure model and for Abaqus support. The current research has been funded by the Swedish Research Council under the project “Numerical Simulation of Respiratory Flow.”
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Larsson, M., Müller, B. (2011). Numerical Simulation of Fluid–Structure Interaction in Human Phonation: Verification of Structure Part. In: Hesthaven, J., Rønquist, E. (eds) Spectral and High Order Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 76. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15337-2_20
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DOI: https://doi.org/10.1007/978-3-642-15337-2_20
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