A semi-implicit discrepancy model of Reynolds stress in a higher-order tensor basis framework for Reynolds-averaged Navier–Stokes simulations

With the rapid development of artificial intelligence, machine learning algorithms are becoming more widely applied in the modification of turbulence models. In this paper, with the aim of improving the prediction accuracy of the Reynolds-averaged Navier–Stokes (RANS) model, a semi-implicit treatment of Reynolds stress anisotropy discrepancy model is developed using a higher-order tensor basis. A deep neural network is constructed and trained based on this discrepancy model. The trained model parameters are embedded in a computational fluid dynamics solver to modify the original RANS model. Modification computations are performed for two cases: one interpolation and one extrapolation of different Reynolds numbers. For these two cases, the ability of the modified model to capture anisotropic features has been improved. Moreover, when compared with the mean velocity of large eddy simulations (LES), the root mean square error of the modified model is significantly lower than the original RANS model. Meanwhile, the modified model can better simulate flow field separation and fluctuation in the shear layer and has better prediction accuracy for the reattachment point and the mean velocity profile compared with the original RANS model. In addition, the modified model also improves the prediction accuracy for the mean pressure coefficient and mean friction coefficient of the underlying wall surface. The previously trained model is also directly performed for the modification computation of the two massive separation periodic hill flows. It is shown that the results simulated by the modified model and LES approach are more consistent in both trend and magnitude than the original RANS model and LES approach.