Finite element approximation of fluid structure interaction using Taylor-Hood and Scott-Vogelius elements

0583300 - MÚ 2025 RIV CZ eng C - Conference Paper (international conference)
Vacek, Karel - Sváček, P.
Finite element approximation of fluid structure interaction using Taylor-Hood and Scott-Vogelius elements.
Topical Problems of Fluid Mechanics. Prague: Institute of Thermomechanics AS CR, v. v. i., 2024 - (Šimurda, D.; Bodnár, T.), s. 232-239. ISBN 978-80-87012-88-8. ISSN 2336-5781.
[Topical Problems of Fluid Mechanics 2024. Prague (CZ), 21.02.2024-23.02.2024]
R&D Projects: GA ČR(CZ) GA22-01591S
Institutional support: RVO:67985840
Keywords : finite element method * arbitrary Lagrangian-Eulerian method * Scott-Vogelius element * Taylor-Hood element
OECD category: Pure mathematics
https://doi.org/10.14311/TPFM.2024.031

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.
Permanent Link: https://hdl.handle.net/11104/0351299