# Article

**Keywords:**

aeroelastic; incompressible; viscous; fluid flow; fluid structure interaction; Navier-Stokes equations; arbitrary Lagrangian-Eulerian form

**Summary:**

In this paper the numerical approximation of aeroelastic response to sudden gust is presented. The fully coupled formulation of two dimensional incompressible viscous fluid flow over a flexibly supported structure is used. The flow is modelled with the system of Navier-Stokes equations written in Arbitrary Lagrangian-Eulerian form and coupled with system of ordinary differential equations describing the airfoil vibrations with two degrees of freedom. The Navier-Stokes equations are spatially discretized by the fully stabilized finite element method. The numerical results are shown.