Numerical simulation of fluid-structure interactions with stabilized finite element method

In this paper the problem of numerical approximation of an interaction of the incompressible viscous flow with a vibrating airfoil is considered. The attention is paid to the practical implementation of the finite element based solver. The underlying mathematical model is based on the incompressible Navier-Stokes equations coupled with the continuity equation. The arbitrary Lagrangian-Eulerian method is used to treat the time dependent domain. The weak formulation of the Navier-Stokes equation is introduced and several important issues are addressed. The numerical method based on the fully stabilized finite element method is described in details. The numerical results are shown. The reliability of the method is discussed.