Deconvolutional artificial neural network (DANN) models are developed for subgrid-scale (SGS) stress in large eddy simulation (LES) of turbulence. The filtered velocities at different spatial points are used as input features of the DANN models to reconstruct the unfiltered velocity. The grid width of the DANN models is chosen to be smaller than the filter width in order to accurately model the effects of SGS dynamics. The DANN models can predict the SGS stress more accurately than the conventional approximate deconvolution method and velocity gradient model in the a priori study: the correlation coefficients can be made larger than 99% and the relative errors can be made less than 15% for the DANN model. In an a posteriori study, a comprehensive comparison of the DANN model, the implicit LES (ILES), the dynamic Smagorinsky model (DSM), and the dynamic mixed model (DMM) shows that the DANN model is superior to the ILES, DSM, and DMM models in the prediction of the velocity spectrum, various statistics of velocity, and the instantaneous coherent structures without increasing the considerable computational cost; the time for the DANN model to calculate the SGS stress is about 1.3 times that of the DMM model. In addition, the trained DANN models without any fine-tuning can predict the velocity statistics well for different filter widths. These results indicate that the DANN framework with the consideration of SGS spatial features is a promising approach to develop advanced SGS models in the LES of turbulence.

In this work, artificial neural network-based nonlinear algebraic models (ANN-NAMs) are developed for the subgrid-scale (SGS) stress in large eddy simulation (LES) of turbulence at the Taylor Reynolds number Reλ ranging from 180 to 250. An ANN architecture is applied to construct the coefficients of the general NAM for the SGS anisotropy stress. It is shown that the ANN-NAMs can reconstruct the SGS stress accurately in the a priori test. Furthermore, the ANN-NAMs are analyzed by calculating the average, root mean square values, and probability density functions of dimensionless model coefficients. In an a posteriori analysis, we compared the performance of the dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and ANN-NAM. The ANN-NAM yields good agreement with a filtered direct numerical simulation dataset for the spectrum, structure functions, and other statistics of velocity. Besides, the ANN-NAM predicts the instantaneous spatial structures of SGS anisotropy stress much better than the DSM and DMM. The NAM based on the ANN is a promising approach to deepen our understanding of SGS modeling in LES of turbulence.

Kinetic energy flux (KEF) is an important physical quantity that characterizes cascades of kinetic energy in turbulent flows. In large-eddy simulation (LES), it is crucial for the subgrid-scale (SGS) model to accurately predict the KEF in turbulence. In this paper, we propose a new eddy-viscosity SGS model constrained by the properly modelled KEF for LES of compressible wall-bounded turbulence. The new methodology has the advantages of both accurate prediction of the KEF and strong numerical stability in LES. We can obtain an approximate KEF by the tensor-diffusivity model, which has a high correlation with the real value. Then, using the artificial neural network method, the local ratios between the real KEF and the approximate KEF are accurately modelled. Consequently, the SGS model can be improved by the product of that ratio and the approximate KEF. In LES of compressible turbulent channel flow, the new model can accurately predict mean velocity profile, turbulence intensities, Reynolds stress, temperature–velocity correlation, etc. Additionally, for the case of a compressible flat-plate boundary layer, the new model can accurately predict some key quantities, including the onset of transitions and transition peaks, the skin-friction coefficient, the mean velocity in the turbulence region, etc., and it can also predict the energy backscatters in turbulence. Furthermore, the proposed model also shows more advantages for coarser grids.

The subgrid-scale stress (SGS) of large-eddy simulation (LES) is modeled by artificial neural network-based spatial gradient models (ANN-SGMs). The velocity gradients at neighboring stencil locations are incorporated to improve the accuracy of the SGS stress. The consideration of the gradient terms in the stencil locations is in a semi-explicit form so that the deployed artificial neural network (ANN) can be considerably simplified. This leads to a much higher LES efficiency compared with previous “black-box” models while still retaining the level of accuracy in the a priori test. The correlation coefficients of the ANN-SGMs can be larger than 0.98 for the filter width in the inertial range. With the current formulation, the significances of the individual modeling terms are transparent, giving clear guidance to the potential condensation of the model, which further improves the LES efficiency. The computational cost of the current ANN-SGM method is found to be two orders lower than previous “black-box” models. In the a posteriori test, the ANN-SGM framework predicts more accurately the flow field compared with the traditional LES models. Both the flow statistics and the instantaneous field are accurately recovered. Finally, we show that the current model can be adapted to different filter widths with sufficient accuracy. These results demonstrate the advantage and great potential of the ANN-SGM framework as an attractive solution to the closure problem in large-eddy simulation of turbulence.

Dynamic iterative approximate deconvolution (DIAD) models with Galilean invariance are developed for subgrid-scale (SGS) stress in the large-eddy simulation (LES) of turbulence. The DIAD models recover the unfiltered variables using the filtered variables at neighboring points and iteratively update model coefficients without any a priori knowledge of direct numerical simulation (DNS) data. The a priori analysis indicates that the DIAD models reconstruct the unclosed SGS stress much better than the classical velocity gradient model and approximate deconvolution model with different filter scales ranging from viscous to inertial regions. We also propose a small-scale eddy viscosity (SSEV) model as an artificial dissipation to suppress the numerical instability based on a scale-similarity-based dynamic method without affecting large-scale flow structures. The SSEV model can predict a velocity spectrum very close to that of DNS data, similar to the traditional implicit large-eddy simulation. In the a posteriori testing, the SSEV-enhanced DIAD model is superior to the SSEV model, dynamic Smagorinsky model, and dynamic mixed model, which predicts a variety of statistics and instantaneous spatial structures of turbulence much closer to those of filtered DNS data without significantly increasing the computational cost. The types of explicit filters, local spatial averaging methods, and initial conditions do not significantly affect the accuracy of DIAD models. We further successfully apply DIAD models to the homogeneous shear turbulence. These results illustrate that the current SSEV-enhanced DIAD approach is promising in the development of advanced SGS models in the LES of turbulence.