Reynolds stress correction by machine learning methods with physical constraints

Summary

For the past three decade, Reynolds Average Navier-Stokes models have been widely used in the industry to simulate complex flows. However, these models suffer from limitations. Indeed there are still large discrepancies in the Reynolds stresses between the RANS model and high-fidelity data provided by DNS or experiments. This paper presents a strategy to correct the Menter SST model using an explicit algebraic model and two different neural networks: an multilayer perceptron (MLP) and a generative adversarial network (GAN). Moreover, in order to preserve the physical properties of the Reynolds stress tensor, we introduce a penalisation term in the loss of the GAN.