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DGFEM for the analysis of airfoil vibrations induced by compressible flow. (English) Zbl 1277.74026
Summary: 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.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76G25 General aerodynamics and subsonic flows
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