A Higher-Order Semi-Lagrangian ALE-FE Method for Fluid-Structure Interaction Problems

Abstract

Fluid-structure interactions (FSI) occur in numerous natural and engineered systems. A particularly important class within the offshore industry is vortex-induced vibration (VIV), especially in the context of riser structural dynamics. This phenomenon arises from the nonlinear interaction between fluid flow and cylindrical structures, often leading to the formation of a von Karman vortex street. As the flow passes a blunt body, alternating vortices form in the wake, generating unsteady lift and drag forces that excite the structure and induce oscillations. To accurately capture the complex dynamics associated with VIV, this study employs the two-dimensional incompressible Navier-Stokes equations formulated within the arbitrary Lagrangian-Eulerian (ALE) framework, which enables large mesh displacements while preserving numerical accuracy. This moving mesh scheme is coupled with a mixed finite element method (FEM) for spatial discretization, with higher-order elements applied to the fluid domain, which automatically satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition. To enhance numerical stability at higher Reynolds numbers, a two-step semi-Lagrangian (SL) scheme is employed.