Computational fluid dynamics (CFD) is an important tool for turbulence research, and Reynolds-averaged Navier−Stokes (RANS) has been widely applied in many applications such as aerospace engineering. The predictive accuracy of RANS is usually significantly impacted by turbulence models, while models used in practical RANS simulations are sometimes not accurate enough. Recently, data driven turbulence modelling has gained its popularity, and different machine learning methods have been introduced to develop turbulence models with enhanced accuracy. In the present study, we review recent developments in data-driven turbulence modelling with the gene-expression-programming (GEP) method. We start with a brief introduction of the GEP method applied to turbulence modelling. The topics discussed in this paper include basic concepts of the GEP algorithm, training frameworks for explicit algebraic stress models and turbulent heat flux models, testing methods for data-driven models, and setup of cost functions. Thereafter, the applications of the GEP method in different areas, e.g.
wake mixing for gas turbines, natural convection between two vertical plates, and jet in cross flow, have been discussed in details. Based on the given results, the trained GEP models are able to improve the predictive accuracy for different key parameters, including the kinetic wake loss and the turbulent heat flux in these cases. Furthermore, as the model equations are explicitly given by the GEP method, the trained models, either the explicit algebraic stress models or the turbulent heat flux models, can be further analyzed. Moreover, models trained with the CFD-driven methods have been applied in practical RANS calculations of different cases, and the results are shown to be accurate and robust in a posteriori
tests. The GEP method has also been applied in sub-grid scale stress modelling in large-eddy simulations and also boundary layer transition, in which the method has demonstrated a great potential in different turbulence modelling areas.