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

Abstract

Reynolds-averaged Navier-Stokes (RANS) equations are presently one of the most popular models for simulating turbulence. Performing RANS simulation requires additional modeling 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 modeling 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 (Ling et al., 2016b) on the turbulent channel flow dataset.

A curated dataset for data-driven turbulence modelling

“… 11 , Fang et al . 12 , and Song et al . 13 all show promise, the results cannot be directly compared—each investigation used a different set of input features and labels, with different numerical settings chosen for feature generation.…”

“…Kaandorp 8 and Kaandorp and Dwight 9 proposed a tensor basis random forest (TBRF) model, which is the random forests analogue to the TBNN proposed by Ling et al 6 . While the different models by Ling et al 6 , Wu et al 7 , Kaandorp and Dwight 9 , Zhu and Dinh 10 , Zhang et al 11 , Fang et al 12 , and Song et al 13 all show promise, the results cannot be directly compared-each investigation used a different set of input features and labels, with different numerical settings chosen for feature generation. For this reason, Duraisamy 14 recently highlighted the need for a benchmark dataset for machine-learnt closure models.…”

Towards Exascale Design of Soft Mesoscale Materials

“…Further speed can be gained by postulating the functional expression of the coarse grained K-tensor in formal analogy with recent work on turbulence modelling [60], i.e. based on the basic symmetries of the problem, which further constrains the functional dependence of K c on the density field.…”

Reservoir computing model of two-dimensional turbulent convection

“…The application of machine learning (ML) methods, in particular of deep neural networks (DNN) [1][2][3][4][5], to fluid flows has transformed the way of processing and analyzing large amounts of data. ML methods are used to parametrize unresolved scales in Reynolds stresses and subgrid scale models for complex physical or geometrical flow configurations at high Reynolds numbers which still remain inaccessible to direct numerical simulations or even large eddy simulations [6][7][8][9][10]. They are also used for the detailed segmentation of complex images [11,12].…”