A construction and training data correction method for deep learning turbulence model of Reynolds averaged Navier–Stokes equations

Abstract

This paper aims at proposing a data-driven Reynolds Averaged Navier–Stokes (RANS) calculation model based on physically constrained deep learning. Using the standard k − ɛ model as the template, part of the source terms in the ɛ equation is replaced by the deep learning model. The simulation results of this new model achieve a high error reduction of 51.7% compared to the standard k − ɛ model. To improve the generality, the accuracy, and the convergence for the undeveloped flow, this paper focuses on optimizing the training process and introducing a data correction method named “coordinate” technology. For the training dataset, the k-field and ɛ-field are automatically corrected by using this technology when the flow state deviates from the theoretical estimation of the standard k − ɛ model. Based on the coordinate technology, a source term of the equation is built by deep learning, and the simulation error is reduced by 6.2% compared to the uncoordinated one. The results confirm that the coordinate technology can effectively adapt to the undeveloped flow where the standard k − ɛ model is not suited and improve the accuracy of the data-driven RANS modeling when dealing with complex flows.