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An ensemble Kalman filter (EnKF)-based mixed model (EnKF-MM) is proposed forthe subgrid-scale (SGS) closure in the large-eddy simulation (LES) ofturbulence. The model coefficients are determined through the EnKF-based dataassimilation technique. The direct numerical simulation (DNS) results arefiltered to obtain the benchmark data for LES. Reconstructing the correctkinetic energy spectrum of the filtered DNS (fDNS) data has been adopted as thetarget for the EnKF to optimize the coefficient of the functional part in themixed model. The proposed EnKF-MM framework is subsequently tested in the LESof both the incompressible homogeneous isotropic turbulence (HIT) and turbulentmixing layer (TML). The performance of LES is comprehensively examined throughthe predictions of the flow statistics including the velocity spectrum, theprobability density functions (PDFs) of the SGS stress, the PDF of the strainrate and the PDF of the SGS energy flux. The structure functions, the evolutionof turbulent kinetic energy, the mean flow and the Reynolds stress profile, andthe iso-surface of the Q-criterion are also examined to evaluate thespatial-temporal predictions by different SGS models. The results of theEnKF-MM framework are consistently more satisfying compared to the traditionalSGS models, including the dynamic Smagorinsky model (DSM), the dynamic mixedmodel (DMM) and the velocity gradient model (VGM), demonstrating its greatpotential in the optimization of SGS models for LES of turbulence.

Ensemble data assimilation-based mixed subgrid-scale model for large-eddy simulations