Deconvolutional artificial neural network models for large eddy simulation of turbulence

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.