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Data-driven turbulence modeling studies have reached such a stage that the fundamental framework is basically settled, but several essential issues remain that strongly affect the performance, including accuracy, smoothness, and…

Fluid Dynamics · Physics 2022-09-21 Yuhui Yin , Yufei Zhang , Haixin Chen , Song Fu

The pressure strain correlation plays a critical role in the Reynolds stress transport modelling. Accurate modelling of the pressure strain correlation leads to proper prediction of turbulence stresses and subsequently the other terms of…

Fluid Dynamics · Physics 2021-03-02 J P Panda , H V Warrior

Machine learning techniques have been applied to enhance turbulence modeling in recent years. However, the "black box" nature of most machine learning techniques poses significant interpretability challenges in improving turbulence models.…

Fluid Dynamics · Physics 2025-08-22 Boqian Zhang , Juanmian Lei

This work presents a review and perspectives on recent developments in the use of machine learning (ML) to augment Reynolds-averaged Navier--Stokes (RANS) and Large Eddy Simulation (LES) models of turbulent flows. Different approaches of…

Fluid Dynamics · Physics 2021-05-19 Karthik Duraisamy

In this paper, a turbulence model based on deep neural network is developed for turbulent flow around airfoil at high Reynolds numbers. According to the data got from the Spalart-Allmaras (SA) turbulence model, we build a neural network…

Fluid Dynamics · Physics 2021-11-29 Xuxiang Sun , Wenbo Cao , Yilang Liu , Linyang Zhu , Weiwei Zhang

The design of film cooling systems relies heavily on Reynolds-Averaged Navier-Stokes (RANS) simulations, which solve for mean quantities and model all turbulent scales. Most turbulent heat flux models, which are based on isotropic diffusion…

Fluid Dynamics · Physics 2019-10-09 Pedro M. Milani , Julia Ling , John K. Eaton

Deep learning (DL)-based Reynolds stress with its capability to leverage values of large data can be used to close Reynolds-averaged Navier-Stoke (RANS) equations. Type I and Type II machine learning (ML) frameworks are studied to…

Fluid Dynamics · Physics 2022-07-28 Chih-Wei Chang , Nam T. Dinh

Generalisability and the consistency of the a posteriori results are the most critical points of view regarding data-driven turbulence models. This study presents a progressive improvement of turbulence models using simulation-driven…

Fluid Dynamics · Physics 2025-03-26 M. J. Rincón , A. Amarloo , M. Reclari , X. I. A. Yang , M. Abkar

The applicability of computational fluid dynamics (CFD) based design tools depend on the accuracy and complexity of the physical models, for example turbulence models, which remains an unsolved problem in physics, and rotor models that…

Fluid Dynamics · Physics 2023-05-09 Shanti Bhushan , Greg W Burgreen , Joshua L Bowman , Ian D Dettwiller , Wesley Brewer

Fluid thermodynamics underpins atmospheric dynamics, climate science, industrial applications, and energy systems. However, direct numerical simulations (DNS) of such systems can be computationally prohibitive. To address this, we present a…

Fluid Dynamics · Physics 2026-02-11 Luca Menicali , Andrew Grace , David H. Richter , Stefano Castruccio

Reynolds-Averaged Navier-Stokes (RANS) models are widely used for turbulent flow simulations due to their computational efficiency, but their accuracy strongly depends on the selected turbulence closure and may vary across the flow domain.…

Numerical Analysis · Mathematics 2026-03-18 Piero Zappi , Anna Ivagnes , Niccolò Tonicello , Gianluigi Rozza

In this paper, a novel zonal machine learning (ML) approach for Reynolds-averaged Navier-Stokes (RANS) turbulence modelling based on the divide-and-conquer technique is introduced. This approach involves partitioning the flow domain into…

Fluid Dynamics · Physics 2024-08-27 Anthony Man , Mohammad Jadidi , Amir Keshmiri , Hujun Yin , Yasser Mahmoudi

This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize…

Fluid Dynamics · Physics 2023-01-24 Hongwei Tang , Yan Wang , Tongguang Wang , Linlin Tian

In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of…

Fluid Dynamics · Physics 2022-11-02 Z. Y. Wang , W. W. Zhang

We present a machine learning-based framework for blending data-driven turbulent closures in the Reynolds-Averaged Navier-Stokes (RANS) equations, aimed at improving their generalizability across diverse flow regimes. Specialized models…

Fluid Dynamics · Physics 2025-03-05 Mourad Oulghelou , Soufiane Cherroud , Xavier Merle , Paola Cinnella

This study proposes a newly-developed deep-learning-based method to generate turbulent inflow conditions for spatially-developing turbulent boundary layer (TBL) simulations. A combination of a transformer and a multiscale-enhanced…

Fluid Dynamics · Physics 2023-03-22 Mustafa Z. Yousif , Meng Zhang , Linqi Yu , Ricardo Vinuesa , HeeChang Lim

Thermal fluid processes are inherently multi-physics and multi-scale, involving mass-momentum-energy transport phenomena. Thermal fluid simulation (TFS) is based on solving conservative equations, for which - except for "first-principle"…

Fluid Dynamics · Physics 2018-11-07 Chih-Wei Chang , Nam T. Dinh

Simulating turbulent flows is crucial for a wide range of applications, and machine learning-based solvers are gaining increasing relevance. However, achieving temporal stability when generalizing to longer rollout horizons remains a…

Machine Learning · Computer Science 2024-12-12 Georg Kohl , Li-Wei Chen , Nils Thuerey

Symbolic regression (SR) methods have been extensively investigated to explore explicit algebraic Reynolds stress models (EARSM) for turbulence closure of Reynolds-averaged Navier-Stokes (RANS) equations. The deduced EARSM can be readily…

Fluid Dynamics · Physics 2024-10-15 Yu Zhang , Kefeng Zheng , Fei Liu , Qingfu Zhang , Zhenkun Wang

Modelling the sudden depressurisation of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including…

Fluid Dynamics · Physics 2021-12-15 David Schmidt , Romit Maulik , Konstantinos G. Lyras