A data-driven approach for the closure of RANS models by the divergence of the Reynolds Stress Tensor
This work addresses the closure problem in turbulence modeling for computational fluid dynamics, offering a potentially more accurate alternative to traditional models, but it appears incremental as it extends existing data-driven approaches to a new target variable.
The paper tackles the closure problem in Reynolds-Averaged Navier-Stokes (RANS) equations by proposing a data-driven model that uses a neural network to predict the divergence of the Reynolds Stress Tensor, ensuring Galilean and rotational invariance. It demonstrates improved accuracy over standard turbulence models in tests like flow in a square duct and over periodic hills, though specific numerical gains are not quantified.
In the present paper a new data-driven model is proposed to close and increase accuracy of RANS equations. The divergence of the Reynolds Stress Tensor (RST) is obtained through a Neural Network (NN) whose architecture and input choice guarantee both Galilean and coordinates-frame rotation. The former derives from the input choice of the NN while the latter from the expansion of the divergence of the RST into a vector basis. This approach has been widely used for data-driven models for the anisotropic RST or the RST discrepancies and it is here proposed for the divergence of the RST. Hence, a constitutive relation of the divergence of the RST from mean quantities is proposed to obtain such expansion. Moreover, once the proposed data-driven approach is trained, there is no need to run any classic turbulence model to close the equations. The well-known tests of flow in a square duct and over periodic hills are used to show advantages of the present method compared to standard turbulence models.