Finite element method analysis of flutter: Comparing Scott–Vogelius and Taylor–Hood elements

Abstract

This paper focuses on the numerical simulation of the fluid–structure interaction (FSI) problem of an incompressible flow and a vibrating airfoil. The fluid flow is governed by the incompressible Navier–Stokes equations. The finite element method (FEM) is employed for the discretization of the weak form of equations. The main attention is paid to comparison of performance for different choices of finite element spaces together with a proper stabilization method. Two choices of the couple of finite element spaces are considered for velocity–pressure approximations. The first one is the standard Taylor–Hood finite element, the second one is the Scott–Vogelius element consisting of continuous piecewise quadratic velocities combined with discontinuous piecewise linear pressures. The barycentric refined mesh is used for the case of the Scott–Vogelius element in order to satisfy the Babuška–Brezzi inf-sup condition. The finite element approximations further require additional stabilization of the dominating convection. Here, the performance of the stream-line upwind Petrov–Galerkin (SUPG) stabilization, the SUPG together with the grad-div stabilization, the streamline-diffusion/local-projection stabilization approach is tested. The numerical results are presented and compared with the available data.