  In recent years, machine learning methods represented by deep neural networks
(DNN) have been a new paradigm of turbulence modeling. However, in the scenario
of high Reynolds numbers, there are still some bottlenecks, including the lack
of high-fidelity data and the convergence and stability problem in the coupling
process of turbulence models and the RANS solvers. In this paper, we propose an
improved ensemble kalman inversion method as a unified approach of data
assimilation and turbulence modeling for separated flows at high Reynolds
numbers. The trainable parameters of the DNN are optimized according to the
given experimental surface pressure coefficients in the framework of mutual
coupling between the RANS equations and DNN eddy-viscosity models. In this way,
data assimilation and model training are combined into one step to get the
high-fidelity turbulence models agree well with experiments efficiently. The
effectiveness of the method is verified by cases of separated flows around
airfoils(S809) at high Reynolds numbers. The results show that through joint
assimilation of vary few experimental states, we can get turbulence models
generalizing well to both attached and separated flows at different angles of
attack. The errors of lift coefficients at high angles of attack are
significantly reduced by more than three times compared with the traditional SA
model. The models obtained also perform well in stability and robustness.
