In the aeronautics or civil engineering communities, stability of structures coupled to real-life flows is often investigated using simplified flow models. Most of them consist in approximating the fluid loads through added mass, stiffness and damping coefficients, determined analytically. If this approach has proven to be of great use in the case of attached flows (e.g. classical flutter instability), more complex flows - involving separated and recirculating areas or shocks - require the use of full fluid model.

In the continuation of Jean-Lou's work, the objective of my thesis is to investigate configurations where the fluid-structure coupling is significantly impacted by such complex flow topologies. Two directions for complexifying the fluid modelisation are being explored : (i) high-Reynolds number effects (ii) 3D effects.

During the first part of this thesis, we revisited the well-known flutter instability of a spring-mounted elongated plate (heaving and pitching movements) in a turbulent flow. The main novelty with respect to previous studies is to perform Linear Stability Analysis using complex fluid models like the full Navier-Stokes equations for laminar flows or RANS modelisation for the turbulent flow. Such models allow to take into account complex flow pattern, like the leading edges recirculation regions, that are present at sufficiently high Reynolds number, for our plates. We compared the predictions of those complex models with the outputs of the classical Theodorsen flutter theory for potential flows. We are currently investigating the non-linear regime of flutter instability, with particular focus on the type of bifurcations that appear (subcritical/supercritical).

â–º More details in our **Coupled-mode flutter**** **webpage**.**

The ambition to go towards 3D fluid-structure is inevitably accompanied by the burden of numerical complexity. In particular, performing Linear Stability Analysis on large 3D configurations is not as straightforward as for reasonable 2D case due to the necessity to use iterative methods. We thus propose numerical methods for performing Linear Stability Analysis on large 3D configurations, first for a laminar fluid flow alone and then for a coupled fluid-structure system. This numerical strategy, based on Augmented Lagrangian preconditioners is an alternative to the widely used Laplace preconditioning and has been implemented in parallel for use on large clusters.

â–º More details in our **Large scale linear systems**** **webpage**.**

On our route towards performing Linear Stability Analysis on large 3D fluid-structure problems, we considered the possibility of using non-conforming FSI formalism. We focused on the so-called Fictitious Domain method and adapted it for stability analysis purposes. The main interest of such non-conforming methods is that the size of the resulting discrete problem is usually much less (at least for external aeroelasticity configurations). We first tested it on the case of rigid structures and could retrieve the classical Vortex-Induced Vibrations instability of a spring-mounted cylinder. Secondly, we considered the case of a flexible structure that showed promising, but more nuanced results.

â–º More details in our **Fictitious Domain and Linearization**** **webpage**.**