Linear and nonlinear sensor placement strategies for mean-flow reconstruction via data assimilation
Stratégies de placement de capteurs linéaires et nonlinéaires pour la reconstruction d'écoulements moyens par assimilation de données
Résumé
Reynolds-averaged Navier–Stokes (RANS)-based data assimilation has proven to be essential in many data-driven approaches, including the augmentation of experimental data and the identification of turbulence model corrections. As dense measurements of the whole mean flow are not always available when performing data assimilation, we here investigate the case where only a few punctual mean velocity measurements are employed to infer the full mean flow. Sensor placement methodologies are developed targeting an enhancement in either (i) the extrapolation of the full mean velocity field from the few punctual measurements or (ii) the identification of the considered model correction, which is here a forcing term in the momentum equations that accounts for the divergence of the Reynolds stress tensor. Concerning the first objective, a sensor placement procedure based on the correct reconstruction of the dominant singular modes of the linearized RANS equations is developed. When focusing on retrieving the model correction, we propose in particular a second-order adjoint-based approach to improve the well posedness of the data assimilation problem. It consists in minimizing the condition number of the Hessian operator that is associated with the cost function to optimize in data assimilation. This procedure allows us to take into account all nonlinearities in the present inverse problem during the optimization of the sensor locations, thus ensuring its effectiveness. Numerical experiments on the reconstruction of the mean flow around a circular cylinder at Re=150 confirm the validity of the developed sensor placement methodologies, which enable a significant improvement in the fidelity of the reconstructed flow with respect to the true one in multiple scenarios in terms of number of sensors and initial network arrangements.
Différentes stratégies de placement de capteurs sont proposées dans le cadre de la reconstruction de champs moyens par assimilation de données variationnelle et l'approche RANS (Reynolds-Averaged Navier-Stokes). Ces méthodologies se concentrent soit directement sur la reconstruction du champ de vitesse complet à partir des données limitées, soit sur l'identification d'une correction aux équations RANS sous la forme d'un terme de forçage pour la quantité de mouvement. Ces développements sont validés en considérant l'écoulement moyen autour d'un cylindre à Re=100.
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