A survey of machine learning wall models for large eddy simulation

Aug 4, 2026

Uploaded by Jiven

A survey investigates wall modeling in large eddy simulations (LES) using data-driven machine learning (ML) methods. Three ML wall models are implemented in an open-source code and evaluated against the equilibrium wall model for half-channel flow across eleven friction Reynolds numbers (Reτ=180–1010). The models are trained on only a few Reynolds numbers to test extrapolation to unseen values. Two supervised models use DNS-based training, while one reinforcement learning model learns within a wall-modeled LES without high-fidelity data. Supervised models capture the law of the wall on both seen and unseen Reynolds numbers with caveats, while the reinforcement learning model shows reasonable accuracy but errors at low and high Reynolds numbers. Error analysis attributes supervised errors to network design and reinforcement errors to state choices and action-map state mismatch.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages19

Reading Time48 min

AccessFree to download

Introduction

Motivation and background

ML vs empirical turbulence models

Need for comparative studies

Scope and approach for ML wall models

arXiv :2211 .03614v1 [physics .flu-dyn] 7 Nov 2022 A survey of machine learning wall models for large eddy simulation Aurélien Vadrot, 1, 􀀃 Xiang I.A. Yang,2, y and Mahdi Abkar 1, z 1 Department of Mechanical and Production Engineering, Aarhus University, 8000 Aarhus C, Denmark 2 Department of Mechanical Engineering, Pennsylvania State University, State College, PA, 16802, USA (Dated: November 8, 2022) This survey investigates wall modeling in large eddy simulations (LES) using data-driven machine learning (ML) techniques. To this end, we implement three ML wall models in an open-source code and compare their performances with the equilibrium wall model in LES of half-channel ﬂow at eleven friction Reynolds numbers between 180 and 1010 . The three models have “seen” ﬂows at only a few Reynolds numbers. We test if these ML wall models can extrapolate to unseen Reynolds numbers. Among the three models, two are supervised ML models, and one is a reinforcement learning ML model. The two supervised ML models are trained against direct numerical simulation (DNS) data, whereas the reinforcement learning ML model is trained in the context of a wallmodeled LES with no access to high-ﬁdelity data. The two supervised ML models capture the law of the wall at both seen and unseen Reynolds numbers—although one model requires re-training and predicts a smaller von Kármán constant. The reinforcement learning model captures the law of the wall reasonably well but has errors at both low (Re􀀜 < 103 ) and high Reynolds numbers (Re􀀜 > 106 ) . In addition to documenting the results, we try to “understand” why the ML models behave the way they behave. Analysis shows that the errors of the supervised ML model is a result of the network design and the errors in the reinforcement learning model arise due to the present choice of the “states” and the mismatch between the neutral line and the line separating the action map. In all, we see promises in data-driven machine learning models. I. INTRODUCTION Machine learning (ML) has been used in a wide range of domains in recent years, including image recognition, market analysis, weather forecast, and others. Computational ﬂuid dynamics (CFD) is not exempt. ML tools were applied in modeling [1–8], computation [9–11], control [12], and optimization [13–15] . An overview of the ML applications in the ﬁeld of ﬂuid dynamics can be found in Refs. [16–18] . Consider turbulence modeling, an old ﬁeld that dates back to at least Prandtl and his mixing length model [19] . In the past 100 years or so, many empirical models have been developed. In the ﬁeld of Reynolds-averaged Navier Stokes (RANS), there exist the Spalart-Allmaras model [20], the SST k 􀀀 ! model [21], the Full Reynolds Stress Model [22, 23], among others. In the ﬁeld of large eddy simulation (LES), there exist the Smagorinksy sub-grid scale (SGS) model [24], the Vreman sub-grid scale model [25], the equilibrium wall model [26], among others. These empirical models and the ones in Refs. [27–29] have survived many independent comparative studies [30–32], are shown to be Galilean invariant, and preserve the known empiricism like the Kolmogorov's theory of small-scale turbulence [33] and the logarithmic law of the wall [34] . Many of these models are now available in commercial and open-source CFD software like Fluent, STARCCM+, and OpenFOAM, and can be picked up and used, as they are, by anyone. However, empirical models are not always suﬃciently accurate. Slotnick et al. [35] noted that the available empirical models fall short in their predictions of separated ﬂows, high-speed ﬂows, and ﬂows with strong heat transfer. The inadequacies of empirical models motivated the development of ML models. In this paper, the term “empirical models” refers to conventional, white-box turbulence models with analytical forms, and the term “ML models” refers to the more recent, black-box turbulence models that usually have no analytical form. Note that t

FAQs

本文研究的核心问题是什么？

研究聚焦于在大涡模拟（LES）中，使用数据驱动的机器学习方法进行壁面建模，并评估其在不同摩擦雷诺数上的表现与外推能力。

论文如何比较不同类型的机器学习壁面模型？

在开源代码中实现三种ML壁面模型，并与LES中的平衡壁面模型对比，考察十一组摩擦雷诺数范围内的结果。

三种ML壁面模型的训练方式有何不同？

两种监督学习模型使用DNS数据进行训练；一种强化学习模型在无高保真数据的条件下，基于壁面建模LES的情境进行训练。

Aug 4, 2026

Uploaded by Jiven