Subgrid-scale model for large-eddy simulation of isotropic turbulent flows using an artificial neural network

• Published in: Computers & fluids 2019-12, Vol.195, p.104319, Article 104319
• Main Authors: Zhou, Zhideng, He, Guowei, Wang, Shizhao, Jin, Guodong
• Format: Article
• Language: English
• Subjects: Artificial neural network; Artificial neural networks; Computational fluid dynamics; Computer simulation; Correlation coefficients; Energy spectra; Energy transfer; Fluid flow; Isotropic turbulent flows; Large eddy simulation; Machine learning; Mathematical models; Neural networks; Scale models; Simulation; Stress tensors; Subgrid-scale model; Tensors; Training; Velocity gradient; Vortices
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2019.104319

•Developing a data-driven subgrid-scale (SGS) model in isotropic turbulent flows.•A single-hidden-layer feedforward artificial neural network (ANN) with Tensorflow.•Taking the filter width into consideration in the training and testing of ANN.•Evaluating the ANN model by both the a priori test and the a posteriori validation.•Using two metrics to evaluate the SGS model in the a priori test. An artificial neural network (ANN) is used to establish the relation between the resolved-scale flow field and the subgrid-scale (SGS) stress tensor, to develop a new SGS model for large-eddy simulation (LES) of isotropic turbulent flows. The data required for training and testing of the ANN are provided by performing filtering operations on the flow fields from direct numerical simulations (DNSs) of isotropic turbulent flows. We use the velocity gradient tensor together with filter width as input features and the SGS stress tensor as the output labels for training the ANN. In the a priori test of the trained ANN model, the SGS stress tensors obtained from the ANN model and the DNS data are compared by computing the correlation coefficient and the relative error of the energy transfer rate. The correlation coefficients are mostly larger than 0.9, and the ANN model can accurately predict the energy transfer rate at different Reynolds numbers and filter widths, showing significant improvement over the conventional models, for example the gradient model, the Smagorinsky model and its dynamic version. A real LES using the trained ANN model is performed as the a posteriori validation. The energy spectrum computed by the improved ANN model is compared with several SGS models. The Lagrangian statistics of fluid particle pairs obtained from the improved ANN model almost approach those from the filtered DNS, better than the results from the Smagorinsky model and dynamic Smagorinsky model.