Topical Problems of Fluid Mechanics


Institute of Thermomechanics AS CR, v.v.i.	CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics	MIO Université du Sud Toulon Var - AMU - CNRS - IRD	Czech Pilot centre ERCOFTAC

Finite Element Approximation of Fluid Structure Interaction Using Taylor-Hood and Scott-Vogelius Elements
Vacek K., Sváček P.
Abstract:
This paper addresses the problem of fluid flow interacting a vibrating solid cylinder described by one degree of freedom system and with fixed airfoil. The problem is described by the incompressible Navier-Stokes equations written in the arbitrary Eulerian-Lagrangian (ALE) formulation. The ALE mapping is constructed with the use of a pseudo-elastic approach. The flow problem is numerically approximated by the finite element method (FEM). For discretization of the fluid flow, the results obtained by both the Taylor-Hood (TH) element and the Scott-Vogelius (SV) finite element are compared. The TH element satisfies the Babuška-Brezzi inf-sup condition, which guarantees the stability of the scheme. In the case of the SV element the mesh, that is created as a barycentric refinement of regular triangulation, is used to satisfy the Babuška-Brezzi condition. The numerical results for two benchmark problems are shown.
Keywords:
finite element method, arbitrary Lagrangian-Eulerian method, Scott-Vogelius element, Taylor-Hood element

Fulltext: PDF DOI: https://doi.org/10.14311/TPFM.2024.031

In Proceedings Topical Problems of Fluid Mechanics 2024, Prague, 2024, Edited by David Šimurda and Tomáš Bodnár, pp. 232 ISBN 978-80-87012-88-8 (Print) ISSN 2336-5781 (Print)