A data-driven approach for the closure of RANS models by the divergence of the Reynolds Stress Tensor

TL;DR

This paper introduces a neural network-based data-driven model to directly estimate the divergence of the Reynolds Stress Tensor in RANS equations, improving accuracy without relying on traditional turbulence models.

Contribution

A novel neural network architecture that guarantees Galilean invariance and frame rotation invariance for modeling the divergence of the Reynolds Stress Tensor in RANS.

Findings

Improved accuracy over standard turbulence models in duct and hill flow tests.

No need for classical turbulence model runs after training.

Effective use of neural networks for turbulence closure modeling.

Abstract

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.