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Knowledge-integrated additive learning for consistent near-wall modelling of turbulent flows

Published online by Cambridge University Press:  13 May 2025

Fengshun Zhang Open the ORCID record for Fengshun Zhang [Opens in a new window] ,
Zhideng Zhou ,
Xiaolei Yang Open the ORCID record for Xiaolei Yang [Opens in a new window]  and
Guowei He Open the ORCID record for Guowei He [Opens in a new window]
Fengshun Zhang
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Zhideng Zhou
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Xiaolei Yang*
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Guowei He
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
Corresponding author: Xiaolei Yang, xyang@imech.ac.cn
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Abstract

Developing a consistent near-wall turbulence model remains an unsolved problem. The machine learning method has the potential to become the workhorse for turbulence modelling. However, the learned model suffers from limited generalisability, especially for flows without similarity laws (e.g. separated flows). In this work, we propose a knowledge-integrated additive (KIA) learning approach for learning wall models in large-eddy simulations. The proposed approach integrates the knowledge in the simplified thin-boundary-layer equation with a data-driven forcing term for the non-equilibrium effects induced by pressure gradients and flow separations. The capability learned from each flow dataset is encapsulated using basis functions with the corresponding weights approximated using neural networks. The fusion of capabilities learned from various datasets is enabled using a distance function, in a way that the learned capability is preserved and the generalisability to other cases is allowed. The additive learning capability is demonstrated via training the model sequentially using the data of the flow with pressure gradient but no separation, and the separated flow data. The capability of the learned model to preserve previously learned capabilities is tested using turbulent channel flow cases. The periodic hill and the 2-D Gaussian bump cases showcase the generalisability of the model to flows with different surface curvatures and different Reynolds numbers. Good agreements with the references are obtained for all the test cases.

JFM classification

Mathematical Foundations: Machine learning Turbulent Flows: Turbulence modelling
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 1011 , 25 May 2025 , R1
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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