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On combining linear stochastic estimation and proper orthogonal decomposition for flow reconstruction

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Abstract

We present an estimation method combining Proper Orthogonal Decomposition (POD) and Linear Stochastic Estimation (LSE). The method is based on a direct mapping of the POD amplitudes from the measurement space to the state space. The method is tested in the turbulent boundary layer for a numerical simulation as well as for experimental data. The goal is to recover the full velocity field on a fine grid from coarse measurements of a single (longitudinal) velocity component. A significant fraction of the turbulent kinetic energy for each component is captured by the estimation. A scale-by-scale analysis shows that lower order modes corresponding to large scales are recovered accurately. Although exact reproduction is not possible at small scales, examination of the spatial and temporal content of the estimated field shows a good statistical agreement with the real field at all scales.

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Acknowledgements

This work was carried out within the framework of the CNRS Research Federation on Council Transports and Mobility, in articulation with the Elast2020 Project supported by the European Community, the French Ministry of Higher Education and Research, and the Hauts de France Regional Council. The authors gratefully acknowledge the support of these institutions. Support for the numerical calculations was provided by IDRIS-GENCI—Project 22062. We are thankful to the referees for their helpful comments.

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Correspondence to Bérengère Podvin.

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Podvin, B., Nguimatsia, S., Foucaut, JM. et al. On combining linear stochastic estimation and proper orthogonal decomposition for flow reconstruction. Exp Fluids 59, 58 (2018). https://doi.org/10.1007/s00348-018-2513-4

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  • DOI: https://doi.org/10.1007/s00348-018-2513-4

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