Convolutional Neural Network Models and Interpretability for the Anisotropic Reynolds Stress Tensor in Turbulent One-dimensional Flows

TL;DR

This paper develops convolutional neural network models to predict the anisotropic Reynolds stress tensor in turbulent flows, enhancing accuracy and interpretability over traditional models and previous neural network approaches.

Contribution

It introduces CNN models for Reynolds stress prediction and provides interpretability techniques to understand model behavior in turbulent flow contexts.

Findings

CNN models accurately predict the anisotropic Reynolds stress tensor

Interpretability techniques reveal physical insights from the CNN models

Models perform well across various one-dimensional turbulent flows

Abstract

The Reynolds-averaged Navier-Stokes (RANS) equations are widely used in turbulence applications. They require accurately modeling the anisotropic Reynolds stress tensor, for which traditional Reynolds stress closure models only yield reliable results in some flow configurations. In the last few years, there has been a surge of work aiming at using data-driven approaches to tackle this problem. The majority of previous work has focused on the development of fully-connected networks for modeling the anisotropic Reynolds stress tensor. In this paper, we expand upon recent work for turbulent channel flow and develop new convolutional neural network (CNN) models that are able to accurately predict the normalized anisotropic Reynolds stress tensor. We apply the new CNN model to a number of one-dimensional turbulent flows. Additionally, we present interpretability techniques that help drive the model design and provide guidance on the model behavior in relation to the underlying physics.