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Data-driven detached-eddy simulations based on explicit algebraic stress expressions for turbulent flows

This work proposes a data-driven explicit algebraic stress-based detached-eddy simulation (DES) method. Despite the widespread use of data-driven methods in model development for both Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulations (LES), their applications to DES remain limited. The challenge mainly lies in the absence of modelled stress data, the requirement for proper length scales in RANS and LES branches, and the maintenance of a reasonable switching behaviour. The data-driven DES method is constructed based on the algebraic stress equation. The control of RANS/LES switching is achieved through the eddy viscosity in the linear part of the modelled stress, under the $\ell^2-ω$ DES framework. Three model coefficients associated with the pressure-strain terms and the LES length scale are represented by a neural network as functions of scalar invariants of velocity gradient. The neural network is trained using velocity data with the ensemble Kalman method, thereby circumventing the requirement for modelled stress data. Moreover, the baseline coefficient values are incorporated as additional reference data to ensure reasonable switching behaviour. The proposed approach is evaluated on two challenging turbulent flows, i.e., the secondary flow in a square duct and the separated flow over a bump. The trained model achieves significant improvements in predicting mean flow statistics compared to the baseline model. This is attributed to improved predictions of the modelled stress. The trained model also exhibits reasonable switching behaviour, enlarging the LES region to resolve more turbulent structures. Furthermore, the model shows satisfactory generalization capabilities for both cases in similar flow configurations.