On suitable inlet boundary conditions for fluid-structure interaction problems in a channel
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We are interested in the numerical solution of a two-dimensional fluid-structure interaction problem. A special attention is paid to the choice of physically relevant inlet boundary conditions for the case of channel closing. Three types of the inlet boundary conditions are considered. Beside the classical Dirichlet and the do-nothing boundary conditions also a generalized boundary condition motivated by the penalization prescription of the Dirichlet boundary condition is applied. The fluid flow is described by the incompressible Navier-Stokes equations in the arbitrary Lagrangian-Eulerian (ALE) form and the elastic body creating a part of the channel wall is modelled with the aid of linear elasticity. Both models are coupled with the boundary conditions prescribed at the common interface.
The elastic and the fluid flow problems are approximated by the finite element method. The detailed derivation of the weak formulation including the boundary conditions is presented. The pseudo-elastic approach for construction of the ALE mapping is used. Results of numerical simulations for three considered inlet boundary conditions are compared. The flutter velocity is determined for a specific model problem and it is shown that the boundary condition with the penalization approach is suitable for the case of the fluid flow in a channel with vibrating walls.
Keywordsflow-induced vibration 2D incompressible Navier-Stokes equations linear elasticity inlet boundary conditions flutter instability
MSC 201076D05 65N30 65N12
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- A. Curnier: Computational Methods in Solid Mechanics. Solid Mechanics and Its Applications 29, Kluwer Academic Publishers Group, Dordrecht, 1994.Google Scholar
- T. A. Davis: Direct Methods for Sparse Linear Systems. Fundamentals of Algorithms 2, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2006.Google Scholar
- N. G. Diez, S. Belfroid, J. Golliard, (eds.): Flow-Induced Vibration & Noise. Proceedings of 11th International Conference on Flow Induced Vibration & Noise. TNO, Delft, The Hague, The NetherlandsGoogle Scholar
- E. H. Dowell: A Modern Course in Aeroelasticity. Solid Mechanics and Its Applications 217, Springer, Cham, 2004.Google Scholar
- M. Feistauer, P. Sváček, J. Horáček: Numerical simulation of fluid-structure interaction problems with applications to flow in vocal folds. Fluid-Structure Interaction and Biomedical Applications (T. Bodnár et al., eds.). Advances in Mathematical Fluid Mechanics, Birkhäuser/Springer, Basel, 2014, pp. 321–393.Google Scholar
- L. Formaggia, N. Parolini, M. Pischedda, C. Riccobene: Geometrical multi-scale modeling of liquid packaging system: an example of scientific cross-fertilization. 19th European Conference on Mathematics for Industry (2016), 6 pages.Google Scholar
- V. Girault, P.-A. Raviart: Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms. Springer Series in Computational Mathematics 5, Springer, Cham, 1986.Google Scholar
- J. Horáček, V. V. Radolf, V. Bula, J. Košina: Experimental modelling of phonation using artificial models of human vocal folds and vocal tracts. Engineering Mechanics 2017 (V. Fuis, ed.). Brno University of Technology, Faculty of Mechanical Engineering, 2017, pp. 382–385.Google Scholar
- J. Horáček, J. G. Švec: Instability boundaries of a vocal fold modelled as a flexibly supported rigid body vibrating in a channel conveying fluid. ASME 2002 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2002, pp. 1043–1054.Google Scholar
- H. Sadeghi, S. Kniesburges, M. Kaltenbacher, A. Schützenberger, M. Döllinger: Computational models of laryngeal aerodynamics: Potentials and numerical costs. Journal of Voice (2018).Google Scholar
- P. Šidlof, J. Kolář, P. Peukert: Flow-induced vibration of a long flexible sheet in tangential flow. Topical Problems of Fluid Mechanics 2018 (D. Šimurda, T. Bodnár, eds.). Institute of Thermomechanics, The Czech Academy of Sciences, Praha, 2018, pp. 251–256Google Scholar
- W. S. Slaughter: The Linearized Theory of Elasticity. Birkhäuser, Boston, 2002.Google Scholar
- J. Valášek, M. Kaltenbacher, P. Sváček: On the application of acoustic analogies in the numerical simulation of human phonation process. Flow, Turbul. Combust. (2018), 1–15Google Scholar
- J. Valášek, P. Sváček, J. Horáček: Numerical solution of fluid-structure interaction represented by human vocal folds in airflow. EPJ Web of Conferences 114 (2016), Article No. 02130, 6 pages.Google Scholar
- J. Valášek, P. Sváček, J. Horáček: On finite element approximation of flow induced vibration of elastic structure. Programs and Algorithms of Numerical Mathematics 18. Proceedings of the 18th Seminar (PANM), 2016. Institute of Mathematics, Czech Academy of Sciences, Praha, 2017, pp. 144–153.zbMATHGoogle Scholar
- S. Zorner: Numerical Simulation Method for a Precise Calculation of the Human Phonation Under Realistic Conditions. Ph.D. Thesis, Technische Uuniversität Wien, 2013.Google Scholar