Space-adaptive simulation of transition and turbulence in shear flows

Sammanfattning: Transitional and turbulent shear flows are ubiquitous, from the boundary layer developing on an aeroplane wing to the flow within the aortic arch. In this thesis, we study wall-bounded and free shear flows through direct numerical simulations. To control numerical errors and represent every flow structure, we implement the adaptive mesh refinement (AMR) technique within a spectral element method code. Using data-driven methods and causality metrics, we explore the fundamental physical mechanisms in various shear flows.The adaptive mesh refinement technique necessitates a precise evaluation of the committed error. Thus, we compare the local spectral error indicator with the dual-weighted adjoint error estimator. The former ensures a more homogeneous refinement, targeting regions with a high-velocity gradient, while the latter is goal-oriented. However, the adjoint error estimator fails in turbulent flows due to the exponential sensitivity of the adjoint linear solution to any perturbation. Alternatively, we introduce a causality-based error indicator that employs the Shannon transfer entropy, i.e. a causality metric arising from information theory, to establish causal relations between the local solution and a specified quantity of interest.Using information-theoretic causality, linear global stability analysis and modal decomposition, we investigate transitional and turbulent coherent structures. In turbulent straight pipe flows, the proper orthogonal decomposition is integrated with the Voronoi diagram to automatically discern between wall-attached and detached eddies. In spatially developing bent pipe flows, we employ the proper orthogonal decomposition to examine the swirl switching phenomenon, the origins of which continue to be a topic of debate. In the context of external flows around a cylinder, we explore two configurations: the Flettner rotor, a rotating cylinder in a wall-bounded shear flow, and the stepped cylinder, namely two cylinders of different diameters joined at one extremity. In the first configuration, we analyse the large-scale motion at the base of the rotor and the local vortex shedding suppression. In the second, we provide an in-depth look at structures arising on the junction surface and in the wake. Additionally, we conduct a global stability analysis with a novel AMR-based approach for some of the aforementioned cases.