Neural Network Models for the Anisotropic Reynolds Stress Tensor in Turbulent Channel Flow

TL;DR

This paper develops and tests modified neural network models to improve the prediction of the anisotropic Reynolds stress tensor in turbulent channel flow, incorporating boundary conditions, Reynolds number effects, and spatial non-locality.

Contribution

It introduces three specific modifications to neural networks for better modeling of Reynolds stress in channel flow, outperforming previous models including the Tensor Basis Neural Network.

Findings

Modified models show increased accuracy over standard neural networks.

The best model combines boundary condition enforcement and Reynolds number injection.

The proposed models outperform the Tensor Basis Neural Network on the dataset.

Abstract

Reynolds-averaged Navier-Stokes (RANS) equations are presently one of the most popular models for simulating turbulence. Performing RANS simulation requires additional modeling for the anisotropic Reynolds stress tensor, but traditional Reynolds stress closure models lead to only partially reliable predictions. Recently, data-driven turbulence models for the Reynolds anisotropy tensor involving novel machine learning techniques have garnered considerable attention and have been rapidly developed. Focusing on modeling the Reynolds stress closure for the specific case of turbulent channel flow, this paper proposes three modifications to a standard neural network to account for the no-slip boundary condition of the anisotropy tensor, the Reynolds number dependence, and spatial non-locality. The modified models are shown to provide increased predicative accuracy compared to the standard neural network when they are trained and tested on channel flow at different Reynolds numbers. The best performance is yielded by the model combining the boundary condition enforcement and Reynolds number injection. This model also outperforms the Tensor Basis Neural Network (Ling et al., 2016) on the turbulent channel flow dataset.