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Article first published online: 20 FEB 2013
Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Special Issue: Partial Differential Equations: Theory, Applications, Simulations
Volume 93, Issue 6-7, pages 387–402, June 2013
How to Cite
Česenek, J., Feistauer, M. and Kosík, A. (2013), DGFEM for the analysis of airfoil vibrations induced by compressible flow. Z. angew. Math. Mech., 93: 387–402. doi: 10.1002/zamm.201100184
Dedicated to Professor Wolfgang L. Wendland on the occasion of his 75th birthday
- Issue published online: 4 JUN 2013
- Article first published online: 20 FEB 2013
- Manuscript Accepted: 7 JAN 2013
- Manuscript Revised: 18 OCT 2012
- Manuscript Received: 19 DEC 2011
- Czech Science Foundation. Grant Number: 201/08/0012
- Ministry of Education, Nečas Center for Mathematical Modelling. Grant Number: LC06052
- Charles University Prague. Grant Numbers: SVV-2012-265316, GAChU 549912
- Compressible Navier-Stokes equations;
- time-dependent domain;
- ALE formulation;
- discontinuous Galerkin method;
- fluid-structure interaction;
- flow induced airfoil vibrations.
The subject of the paper is the numerical simulation of the interaction of two-dimensional compressible viscous flow and a vibrating airfoil. A solid airfoil with two degrees of freedom performs rotation around an elastic axis and oscillations in the vertical direction. The numerical simulation consists of the solution of the Navier-Stokes system by the discontinuous Galerkin method coupled with a system of nonlinear ordinary differential equations describing the airfoil motion. The time-dependent computational domain and a moving grid are taken into account by the arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations. The developed method is robust with respect to the magnitude of the Mach number and Reynolds number. Its applicability is demonstrated by numerical experiments.