We apply the gene-expression programing (GEP) method to develop subgrid-scale models for large-eddy simulations (LESs) of turbulence. The GEP model is trained based on Galilean invariants and tensor basis functions, and the training data are from direct numerical simulation (DNS) of incompressible isotropic turbulence. The model trained with GEP has been explicitly tested, showing that the GEP model can not only provide high correlation coefficients in a priori tests but also show great agreement with filtered DNS data when applied to LES. Compared to commonly used models like the dynamic Smagorinsky model and the dynamic mixed model, the GEP model provides significantly improved results on turbulence statistics and flow structures. Based on an analysis of the explicitly given model equation, the enhanced predictions are related to the fact that the GEP model is less dissipative and that it introduces high-order terms closely related to vorticity distribution. Furthermore, the GEP model with the explicit equation is straightforward to be applied in LESs, and its additional computational cost is substantially smaller than that of models trained with artificial neural networks with similar levels of predictive accuracies in a posteriori tests.
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