  An ensemble Kalman filter (EnKF)-based mixed model (EnKF-MM) is proposed for
the subgrid-scale (SGS) closure in the large-eddy simulation (LES) of
turbulence. The model coefficients are determined through the EnKF-based data
assimilation technique. The direct numerical simulation (DNS) results are
filtered to obtain the benchmark data for LES. Reconstructing the correct
kinetic energy spectrum of the filtered DNS (fDNS) data has been adopted as the
target for the EnKF to optimize the coefficient of the functional part in the
mixed model. The proposed EnKF-MM framework is subsequently tested in the LES
of both the incompressible homogeneous isotropic turbulence (HIT) and turbulent
mixing layer (TML). The performance of LES is comprehensively examined through
the predictions of the flow statistics including the velocity spectrum, the
probability density functions (PDFs) of the SGS stress, the PDF of the strain
rate and the PDF of the SGS energy flux. The structure functions, the evolution
of turbulent kinetic energy, the mean flow and the Reynolds stress profile, and
the iso-surface of the Q-criterion are also examined to evaluate the
spatial-temporal predictions by different SGS models. The results of the
EnKF-MM framework are consistently more satisfying compared to the traditional
SGS models, including the dynamic Smagorinsky model (DSM), the dynamic mixed
model (DMM) and the velocity gradient model (VGM), demonstrating its great
potential in the optimization of SGS models for LES of turbulence.
