On reliability of finite element method in fluid-structure interaction problems

Abstract. In this paper we are concerned with numerical methods for fluid-structure interaction (FSI) problems and with their verification and validation. The fluid-structure interaction modelling is very complicated problem, where the most complicated and cruicial part is modelling of the fluid flow. Therefore the main interest of this paper is the numerical approximation of two dimensional incompressible viscous fluid over a flexibly supported profile. In technical problems the relevant Reynolds numbers are usually very high (104 − 106) and the fluid flow is turbulent. The correct numerical approximation requires very fine mesh refining as well as very small time steps involved in the computation. On the other hand in many technical applications the Reynolds Averaged NavierStokes equations are being used together with a suitable turbulence model. Here, both (laminar) Navier-Stokes equations as well as Reynolds Averaged Navier-Stokes equations are considered, numerically approximated by the Finite Element Method (FEM), stabilized by Galerkin-LeastSquares technique, and the obtained solution compared to the experimental data.