Artificial neural network-based spatial gradient models for large-eddy simulation of turbulence

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.