• 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.