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Ensemble-variational assimilation of statistical data in large-eddy simulation

Vincent Mons

Yifan Du and Tamer A. Zaki*

  • DAAA, ONERA, Université Paris Saclay, F-92190 Meudon, France and Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA

  • Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA

  • *t.zaki@jhu.edu
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Phys. Rev. Fluids 6, 104607 – Published 21 October, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.104607

Abstract

A nonintrusive data assimilation methodology is developed to improve the statistical predictions of large-eddy simulations (LES). The ensemble-variational (EnVar) approach aims to minimize a cost function that is defined as the discrepancy between LES predictions and reference statistics from experiments or, in the present demonstration, independent direct numerical simulations (DNS). This methodology is applied to adjust the Smagorinsky subgrid model and obtain data assimilated LES (DA-LES) which accurately estimate the statistics of turbulent channel flow. To separately control the mean and fluctuations of the modeled subgrid tensor, and ultimately the first- and second-order flow statistics, two types of model corrections are considered. The first one optimizes the wall-normal profile of the Smagorinsky coefficient, while the second one introduces an adjustable steady forcing in the momentum equations to independently act on the mean flow. Using these two elements, the data assimilation procedure can satisfactorily modify the subgrid model and accurately recover reference flow statistics. In a posteriori testing, the retrieved subgrid model significantly outperforms more elaborate baseline models such as dynamic and mixed models. The robustness of the present data assimilation methodology is assessed by changing the Reynolds number and considering grid resolutions that are away from usual recommendations. Taking advantage of the stochastic formulation of EnVar, the developed framework also provides the uncertainty of the retrieved model.

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Phys. Rev. Fluids 6, 104607– Published 21 October, 2021
  • Received 11 May 2021
  • Accepted 21 September 2021
Article part of CHORUS
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