Benosman, Mouhacine; Borggaard, Jeff Data-driven robust state estimation for reduced-order models of 2D Boussinesq equations with parametric uncertainties. (English) Zbl 1521.76318 Comput. Fluids 214, Article ID 104773, 15 p. (2021). Summary: A robust, low-order POD-based state estimator, also known as an observer, for the challenging fluid-dynamics test-case of uncertain 2D Boussinesq equations is presented in this paper. The observer design is based on the methodology recently introduced by the \(authors^1\), which incorporates robustness to bounded model uncertainties, and data-driven auto-tuning of the observer gains. An extensive numerical study on the 2D Boussinesq equations with parametric uncertainties demonstrates the performance of our observer. The reported numerical results show that the proposed observer allows estimation of the complete temperature and velocity fields from a reduced number of measurements. It is also shown that the proposed observer is robust to changes or errors in the value of the Reynolds number. In other words, we show that we can design the observer based on an assumed uncertain value for the Reynolds number, and be able to estimate the temperature and velocity solutions corresponding to actual Reynolds number. MSC: 76M10 Finite element methods applied to problems in fluid mechanics 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 76D55 Flow control and optimization for incompressible viscous fluids Keywords:thermo-fluid flow state estimation; 2D Boussinesq equations; uncertain Reynolds number; reduced-order models; POD; robustness; data-driven learning; extremum-seeking application PDFBibTeX XMLCite \textit{M. Benosman} and \textit{J. Borggaard}, Comput. Fluids 214, Article ID 104773, 15 p. 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