Data-Driven Adverse Pressure Gradient Correction for Turbulence Model

The Spalart–Allmaras (SA) model is widely used in engineering turbulence simulations. It has been calibrated using the logarithmic law and provides sufficient accuracy in zero pressure gradient (ZPG) turbulent boundary layer (TBL) but shows poor performance in the turbulence with adverse pressure gradient (APG), especially in separated flows. In this paper, the distribution of the important variables and functions of the SA model is studied. It is found that, in APG TBL, the original SA model exhibits significant errors and encounters a multiple-value problem of the f_w function in the destruction term. A new feature is proposed based on the gradient of eddy viscosity to characterize the pressure gradient and history effects of TBL, overcoming the multiple-value problem. A new algebraic expression of the f_w function, as shown in Eq. (21), is established by combining neural networks and symbolic regression. The results show that the new model provides good generalization for nine different flows outside the training set, not only maintaining the good behaviors of the original SA model in ZPG, but also enhancing the accuracy of separated flows.