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\begin{document}

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\begin{center}{\bf Discontinuous Galerkin method for interaction of compressible flow and structures\\

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M. Feistauer, V. Ku\v cera, J. Prokopov\'a\\

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Charles University Prague}\\

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e-mail: feist@karlin.mff.cuni.cz
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The subject of this paper is the numerical simulation of the interaction of two-dimensional
compressible  flow and  structures. Namely, the interaction with a vibrating airfoil or a channel with a moving wall will be considered. The gas flow is described by the Euler or Navier-Stokes equations. They will be discretized by the discontinuous Galerkin finite element method (DGFEM) using piecewise polynomial discontinuous approximations written in the ALE form. We use a special treatment of boundary conditions, shock capturing, special semi-implicit time discretization and isoparametric elements at curved boundaries, allowing the solution of flow with a wide range of Mach numbers.  A
solid airfoil with two degrees of freedom can rotate around the elastic
axis and oscillate in the vertical direction. Its motion is described by a system of  two second-order ordinary differential equations discretized by the Runge-Kutta method, coupled with the DGFEM for the solution of the flow problem. In the case of a channel flow we assume that a part of one wall can oscillate. 
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