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                <term xml:lang="en">Turbulent flow</term>
                <term xml:lang="en">Hyperreduction</term>
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              <p>To monitor in real-time systems evolving in a fluid flow, it is attractive to accurately estimate the flow field over time with limited computational resources. Possible applications such as antifreeze towers, wind turbines, or hydrofoils operate in turbulent flows. A previous work has defined the RedLUM methodology to solve such problems. It showed good results for 3D moderate turbulent unsteady flows spanning from Re=100 up to Re=300. The method builds a stochastic reduced-order model from the Navier-Stokes equation under location uncertainty to decrease the dimension size of the problem. And a fully non-linear data assimilation procedure uses a few measurements to improve the prediction. Recent improvements made it possible to deal with more turbulent flows. The Smagorinsky LES model solves the dynamic of these flows. However, it includes a nonlinearity that remains in the reduced model. A special treatment known as hyperreduction must be performed to preserve the benefit of dimension reduction. We enhanced the Discrete Empirical Interpolation Method to model its approximation error stochastically. The results of a test case at Re=3900 are displayed. They highlight the potential of coupling a low-dimensional physical generative model with data assimilation using very few measurements.</p>
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