A Finite Element Method Coupled with a Semi-Lagrangian Scheme for Turbulent Fluid-Structure Interactions

Abstract

Fluid-structure interaction (FSI) problems are present in multiple engineering fields such as aerospace, offshore and biomedical. It is also a phenomenon observed in natural systems, such as bird flight and swimming fish dynamics. A specific type of FSI is known as vortex-induced vibrations (VIV) and this phenomenon occurs because the fluid flow around bluff bodies generates a von-Kárman vortex street. This vortex shedding process generates oscillating lift and drag forces which excite the immersed body and are responsible for a drastic shift in dynamical behaviour. Since real world applications of VIV mostly happen under turbulent flows and in order to accurately model this intricate phenomenon, this work employs the bidimensional incompressible Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations within the arbitrary Lagrangian-Eulerian (ALE) framework. This reference frame was adopted as it combines the best qualities of the Eulerian and Lagrangian descriptions (Donea et al., 2004). And it allows for the inclusion of moving boundaries within the global domain. The finite element method (FEM) has been at the forefront of simulation methods employed to study FSI, (Zienkiewicz et al., 2014). Hence, the spatial discretization of the governing equations is done by employing higher-order quadrilateral elements which satisfy the Ladyzhenskaya-Babuška-Brezzi (LBB) condition. Thus, no artificial stabilization procedures are required in order to obtain a stable solution for the discrete saddle-point problem.