A higher-order semi-Lagrangian mixed finite element methodology in an arbitrary Lagrangian-Eulerian framework for vortex-induced vibrations of rigid structures

Abstract

Vortex-induced vibrations (VIV) arise from the interaction between bluff structures and unsteady vortex shedding. This work presents a numerical framework for solving the two-dimensional incompressible Navier- Stokes equations in an arbitrary Lagrangian-Eulerian formulation. The equations are discretized using the Galerkin finite element method with an inf-sup stable second-order element, avoiding additional stabilization. Two semi-Lagrangian formulations are employed for the material derivative: a two-step scheme (SL2) and a ynchronization region and the variation of the aerodynamic coefficients with forcing frequency. For a elastically supported cylinder, lock-in occurs roughly in between 80 < Re < 140, with a maximum cros flow amplitude of approximately 0.6D. Three-cylinder triangular and four-cylinder square arrangements are subsequently investigated. The downstream cylinders exhibit up to 2.9 times larger lift fluctuations and ap proximately 39%-47% larger cross-flow amplitudes than the upstream cylinders. Overall, both semi-Lagrangiar schemes capture the principal aerodynamic and structural characteristics of single- and multiple-cylinder VIV configurations.