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.

中文翻译：

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湍流通道流中各向异性雷诺应力张量的神经网络模型

雷诺平均纳维-斯托克斯 (RANS) 方程是目前最流行的湍流模拟模型之一。执行 RANS 仿真需要对各向异性雷诺应力张量进行额外建模，但传统的雷诺应力闭合模型只能产生部分可靠的预测。最近，涉及新型机器学习技术的雷诺各向异性张量的数据驱动湍流模型引起了相当大的关注并得到了迅速发展。本文针对湍流通道流动的特定情况对雷诺应力闭合进行建模，提出了对标准神经网络的三种修改，以说明各向异性张量的无滑移边界条件、雷诺数相关性和空间非局域性. 与标准神经网络相比，修改后的模型在不同雷诺数下对通道流进行训练和测试时，显示出更高的预测精度。结合边界条件强制和雷诺数注入的模型产生了最佳性能。该模型也优于 Ling 等人的张量基础神经网络。[Reynolds 使用具有嵌入式不变性的深度神经网络对湍流进行平均建模。J 流体机械。2016;807:155-166] 在湍流通道流数据集上。该模型也优于 Ling 等人的张量基础神经网络。[Reynolds 使用具有嵌入式不变性的深度神经网络对湍流进行平均建模。J 流体机械。2016;807:155-166] 在湍流通道流数据集上。该模型也优于 Ling 等人的张量基础神经网络。[Reynolds 使用具有嵌入式不变性的深度神经网络对湍流进行平均建模。J 流体机械。2016;807:155-166] 在湍流通道流数据集上。