A Physics Informed Machine Learning Approach for Reconstructing Reynolds Stress Modeling Discrepancies Based on DNS Data

TL;DR

This paper introduces a physics-informed machine learning method using random forests to predict discrepancies in Reynolds stresses from RANS models, trained on DNS data, to improve turbulence modeling accuracy.

Contribution

The paper presents a novel data-driven approach that incorporates physics knowledge to predict Reynolds stress discrepancies, enhancing RANS model predictions across different flow scenarios.

Findings

High accuracy in Reynolds stress discrepancy predictions.

Effective transferability to different flow geometries.

Improved turbulence modeling for industrial flows.

Abstract

Turbulence modeling is a critical component in numerical simulations of industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations. However, after decades of efforts in the turbulence modeling community, universally applicable RANS models with predictive capabilities are still lacking. Recently, data-driven methods have been proposed as a promising alternative to the traditional approaches of turbulence model development. In this work we propose a data-driven, physics-informed machine learning approach for predicting discrepancies in RANS modeled Reynolds stresses. The discrepancies are formulated as functions of the mean flow features. By using a modern machine learning technique based on random forests, the discrepancy functions are first trained with benchmark flow data and then used to predict Reynolds stresses discrepancies in new flows. The method is used to predict the Reynolds stresses in the flow over periodic hills by using two training flow scenarios of increasing difficulties: (1) the flow in the same periodic hills geometry yet at a lower Reynolds number, and (2) the flow in a different hill geometry with a similar recirculation zone. Excellent predictive performances were observed in both scenarios, demonstrating the merits of the proposed method. Improvement of RANS modeled Reynolds stresses enabled by the proposed method is an important step towards predictive turbulence modeling, where the ultimate goal is to predict the quantities of interest (e.g., velocity field, drag, lift) more accurately by solving RANS equations with the Reynolds stresses obtained therefrom.