Abstract
The paper deals with the discontinuous Galerkin method (DGM) for the solution of compressible Navier-Stokes equations in the ALE form in time-dependent domains combined with the solution of linear and nonlinear dynamic elasticity. The developed methods are oriented to fluid-structure interaction (FSI), particularly to the simulation of air flow in a time-dependent domain representing vocal tract and vocal folds vibrations. We compare results obtained with the aid of linear and nonlinear elasticity models. The results show that it is more adequate to use the nonlinear elasticity St. Venant-Kirchhoff model in contrast to the linear elasticity model.
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References
P. G. Ciarlet, Mathematical Elasticity, Volume I, Three-Dimensional Elasticity, Volume 20 of Studies in Mathematics and its Applications, Elsevier Science Publishers B.V., Amsterdam (1988)
V. Dolejší, M. Feistauer, Discontinuous Galerkin method – Analysis and applications to compressible flow, Springer, Cham (2015)
Acknowledgements
This research was supported under the grant of the Czech Science Foundation No. 19-04477S. The research of M. Balázsová was also supported by the Charles University, project SVV-2017-260455.
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Feistauer, M., Balázsová, M., Horáček, J. (2021). ALE Space-Time Discontinuous Galerkin Method for the Interaction of Compressible Flow with Linear and Nonlinear Dynamic Elasticity and Applications to Vocal Fold Vibrations. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_40
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DOI: https://doi.org/10.1007/978-3-030-55874-1_40
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