On the solution of fluid-structure interaction problems

The subject of the lecture is the finite element solution of fluid-structure interaction problems. Our main attention will be paid to the simulation of flow induced airfoil vibrations. A solid airfoil with two degrees of freedom, which can rotate around the elastic axis and oscillate in the vertical direction, is considered. The numerical simulation consists of the finite element solution of the Navier-Stokes equations coupled with the system of ordinary differential equations describing the airfoil motion. The time dependent computational domain and a moving grid are taken into account with the aid of the Arbitrary Lagrangian- Eulerian (ALE) formulation of the Navier-Stokes equations. The time discretization is carried out by the backward difference formula. In space the conforming stabilized finite element method is used. As a result a sufficiently accurate and robust method is developed, which is applied to the case of flow induced airfoil vibrations with large amplitudes after loosing the aeroelastic stability. The developed method was tested on several problems analyzed also experimentally in a wind tunnel.