Neural network models for the anisotropic Reynolds stress tensor in turbulent channel flow

2019/09/09 by Rui Fang, David Sondak, Pavlos Protopapas +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Anisotropy #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometry #Heat Transfer Mechanisms #K-epsilon turbulence model #K-omega turbulence model #Mathematics #Mechanics #Nuclear Engineering Thermal-Hydraulics #Optics #Physics #Reynolds number #Reynolds stress #Reynolds stress equation model #Statistical physics #Tensor (intrinsic definition) #Turbulence #physics.comp-ph #physics.flu-dyn

paper · pdf · doi:10.1080/14685248.2019.1706742

arxiv created 2019/09/09 · openalex publication_date 2019/12/24 · arxiv updated 2020/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Reynolds-averaged Navier-Stokes (RANS) equations are presently one of the most popular models for simulating turbulence. Performing RANS simulation requires additional modelling for the anisotropic Reynolds stress tensor, but traditional Reynolds stress closure models lead to only partially reliable predictions. Recently, data-driven turbulence models for the Reynolds anisotropy tensor involving novel machine learning techniques have garnered considerable attention and have been rapidly developed. Focusing on modelling the Reynolds stress closure for the specific case of turbulent channel flow, this paper proposes three modifications to a standard neural network to account for the no-slip boundary condition of the anisotropy tensor, the Reynolds number dependence, and spatial non-locality. The modified models are shown to provide increased predicative accuracy compared to the standard neural network when they are trained and tested on channel flow at different Reynolds numbers. The best performance is yielded by the model combining the boundary condition enforcement and Reynolds number injection. This model also outperforms the Tensor Basis Neural Network in Ling et al. [Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J Fluid Mech. 2016;807:155–166] on the turbulent channel flow dataset.

Citations

• Adam: A Method for Stochastic Optimization
• Kinetic theory of turbulence modeling: smallness parameter, scaling and microscopic derivation of Smagorinsky model
• ImageNet classification with deep convolutional neural networks
• Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• An overview of gradient descent optimization algorithms
• Mastering the game of Go without human knowledge
• Turbulence Modeling in the Age of Data
• A Universal Fractional Model of Wall-Turbulence
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Deep learning

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