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Field inversion and machine learning are implemented in this study todescribe three-dimensional separation flow around an axisymmetric hill andaugment the Spart-Allmaras model. The discrete adjoint method is used to solvethe field inversion problem, and an artificial neural network is used as themachine learning model. A validation process for field inversion is proposed toadjust the hyperparameters and obtain a physically acceptable solution. Thefield inversion result shows that the non-equilibrium turbulence effects in theboundary layer upstream of the mean separation line and in the separating shearlayer dominate the flow structure in the 3-D separating flow, which agrees withprior physical knowledge. However, the effect of turbulence anisotropy on themean flow appears to be limited. Two approaches are proposed and implemented inthe machine learning stage to overcome the problem of sample imbalance whilereducing the computational cost during training. The results are allsatisfactory, which proves the effectiveness of the proposed approaches.

Data augmented turbulence modeling for three-dimensional separation flows