[Paper Review] Are Discrepancies in RANS Modeled Reynolds Stresses Random?

Heng Xiao, Jinlong Wu+2 more|arXiv (Cornell University)|Jun 27, 2016

Probabilistic and Robust Engineering Design15 references3 citations

TL;DR

This study investigates whether discrepancies in RANS-modeled Reynolds stresses are predictable or random using a random forest regression model. The results show these discrepancies are largely explainable by mean flow features, indicating they are universal and extrapolatable across similar flows—offering a data-driven pathway to improve RANS model accuracy.

ABSTRACT

In the turbulence modeling community, significant efforts have been made to quantify the uncertainties in the Reynolds-Averaged Navier--Stokes (RANS) models and to improve their predictive capabilities. Of crucial importance in these efforts is the understanding of the discrepancies in the RANS modeled Reynolds stresses. However, to what extent these discrepancies can be predicted or whether they are completely random remains a fundamental open question. In this work we used a machine learning algorithm based on random forest regression to predict the discrepancies. The success of the regression--prediction procedure indicates that, to a large extent, the discrepancies in the modeled Reynolds stresses can be explained by the mean flow feature, and thus they are universal quantities that can be extrapolated from one flow to another, at least among different flows sharing the same characteristics such as separation. This finding has profound implications to the future development of RANS models, opening up new possibilities for data-driven predictive turbulence modeling.

Motivation & Objective

• To determine whether discrepancies in RANS-modeled Reynolds stresses are random or predictable.
• To assess whether these discrepancies can be explained by underlying mean flow characteristics.
• To evaluate the feasibility of extrapolating stress discrepancies across different flows with similar features, such as separation.
• To explore the potential for data-driven modeling of RANS uncertainties using machine learning.
• To establish whether discrepancies are universal enough to support generalizable predictive models in turbulence simulation.

Proposed method

• A random forest regression algorithm was trained on data from RANS simulations to predict discrepancies in modeled Reynolds stresses.
• Input features included mean flow variables such as velocity gradients, pressure gradients, and turbulence intensity.
• The model was validated across multiple canonical turbulent flow cases, including flows with adverse pressure gradients and separation.
• Generalization performance was tested by applying the model trained on one flow to predict discrepancies in another flow with similar characteristics.
• The algorithm's predictive capability was assessed using standard regression metrics such as R-squared and mean absolute error.
• The approach leveraged the non-linear pattern recognition strength of random forests to capture complex dependencies between mean flow and stress modeling errors.

Experimental results

Research questions

• RQ1 Can discrepancies in RANS-modeled Reynolds stresses be predicted using mean flow features?
• RQ2 To what extent are these discrepancies deterministic versus random?
• RQ3 Can a machine learning model trained on one flow accurately predict stress discrepancies in another flow with similar physics, such as separation?
• RQ4 Are the discrepancies in Reynolds stress modeling universal across flows with comparable features?
• RQ5 Can data-driven methods reduce uncertainty in RANS models by learning from existing simulation data?

Key findings

• The random forest regression model successfully predicted Reynolds stress discrepancies with high accuracy, indicating they are not purely random.
• Discrepancies were strongly correlated with mean flow features such as velocity and pressure gradients.
• The model demonstrated generalization capability across different flows sharing similar characteristics, such as flow separation.
• The results suggest that discrepancies in RANS models are universal and can be extrapolated across similar flow configurations.
• The study demonstrates that machine learning can effectively learn and predict modeling errors in RANS simulations using only mean flow data.
• These findings open new pathways for developing data-driven, uncertainty-aware RANS models with improved predictive fidelity.