Application of finite element method in aeroelasticity

The subject of this paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil, which can rotate around the elastic axis and oscillate in the vertical direction. The numerical simulation consists of the finite element approximation of the Navier–Stokes equations coupled with the system of ordinary differential equations describing the airfoil motion. The arbitrary Lagrangian–Eulerian (ALE) formulation of the Navier–Stokes equations, stabilization the finite element discretization and coupling of both models is discussed. Moreover, the Reynolds averaged Navier–Stokes (RANS) system of equations together with the Spallart–Almaras turbulence model is also discussed. The computational results of aeroelastic calculations are presented and compared with the NASTRAN code solutions.