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Reynolds-averaged Navier-Stokes (RANS) simulations have found widespread use in engineering applications, yet their accuracy is compromised, especially in complex flows, due to imprecise closure term estimations. Machine learning advancements have opened new avenues for turbulence modeling by extracting features from high-fidelity data to correct RANS closure terms. This method entails establishing a mapping relationship between the mean flow field and the closure term through a designated algorithm. In this study, the k - ω SST model serves as the correction template. Leveraging a neural network algorithm, we enhance the predictive precision in separated flows by forecasting the desired learning target. We formulate linear terms by approximating the high-fidelity closure (from Direct Numerical Simulation) based on the Boussinesq assumption, while residual errors (referred to as nonlinear terms) are introduced into the momentum equation via an appropriate scaling factor. Utilizing data from periodic hills flows encompassing diverse geometries, we train two neural networks, each possessing comparable structures, to predict the linear and nonlinear terms. These networks incorporate features from the minimal integrity basis and mean flow. Through generalization performance tests, the proposed data-driven model demonstrates effective closure term predictions, mitigating significant overfitting concerns. Furthermore, the propagation of the predicted closure term to the mean velocity field exhibits remarkable alignment with the high-fidelity data, thus affirming the validity of the current framework. In contrast to prior studies, we notably trim down the total count of input features to 12, thereby simplifying the task for neural networks and broadening its applications to more intricate scenarios involving separated flows.
Chen et al. (Wed,) studied this question.