Spatially multi-scale artificial neural network model for large eddy simulation of compressible isotropic turbulence

In this work, subgrid-scale (SGS) stress and SGS heat flux of compressible isotropic turbulence are reconstructed by a spatially multi-scale artificial neural network (SMSANN). The input features of the SMSANN model are based on the first order derivatives of the primary and secondary filtered variables at different spatial locations. The SMSANN model performs much better than the gradient model in the a priori test, including the correlation coefficients and relative errors. Specifically, the correlation coefficients of the SGS stress and SGS heat flux can be larger than 0.997 and the relative errors of the SGS stress and SGS heat flux can be smaller than 0.08 for the SMSANN model. In an a posteriori analysis, the performance of the SMSANN model has been evaluated by a detailed comparison of the results of the SMSANN model and the dynamic mixed model (DMM) at a grid resolution of 64(3) with the Taylor Reynolds number Re-lambda ranging from 180 to 250. The SMSANN model shows an advantage over the DMM in the prediction of the spectra of velocity and temperature. Besides, the SMSANN model can accurately reconstruct the statistical properties of velocity and temperature and the instantaneous flow structures. An artificial neural network with consideration of spatial multiscale can deepen our understanding of large eddy simulation modeling.