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We introduce a novel recursive process to a neural-network-basedsubgrid-scale (NN-based SGS) model for large eddy simulation (LES) of highReynolds number turbulent flow. This process is designed to allow an SGS modelto be applicable to a hierarchy of different grid sizes without requiring anexpensive filtered direct numerical simulation (DNS) data: 1) train an NN-basedSGS model with filtered DNS data at a low Reynolds number; 2) apply the trainedSGS model to LES at a higher Reynolds number; 3) update this SGS model withtraining data augmented with filtered LES (fLES) data, accommodating coarserfilter size; 4) apply the updated NN to LES at a further higher Reynoldsnumber; 5) go back to 3) until a target (very coarse) filter size divided bythe Kolmogorov length scale is reached. We also construct an NN-based SGS modelusing a dual NN architecture whose outputs are the SGS normal stresses for oneNN and the SGS shear stresses for the other NN. The input is composed of thevelocity gradient tensor and grid size. Furthermore, for the application of anNN-based SGS model trained with one flow to another flow, we modify the NN byeliminating bias and introducing leaky rectified linear unit function as anactivation function. The present recursive SGS model is applied to forcedhomogeneous isotropic turbulence (FHIT), and successfully predicts FHIT at highReynolds numbers. The present model trained from FHIT is also applied todecaying homogeneous isotropic turbulence, and shows an excellent predictionperformance.

A recursive neural-network-based subgrid-scale model for large eddy simulation: application to homogeneous isotropic turbulence