Numerous current and future technological devices may benefit from the fundamental understanding of the fluid instabilities leading to Vortex Induced Vibrations (VIV). Energy harvesting devices are conceived to extract the mechanical energy of the flow by taking advantage of a fluid-structure instability that leads to a cyclic displacement of the structure. Herein, we propose a Linearised Eulerian-based Arbitrary Lagrangian Eulerian (L-ALE) method in order to rationalize the Eulerian and the Lagrangian character of the flow and structural variables, respectively. We first demonstrate that our method faithfully reproduces previous numerical results reported in the literature. Then, we study the flow configurations of N=2 cylinders, in terms of the distinct fluid-structure instabilities and spatio-temporal properties of the global unstable modes.