Neural-network-based large eddy simulation of flow over a backward facing step

Large eddy simulation (LES) of turbulent flow over a backward facing step is performed using a neural-network-based subgrid-scale (SGS) model. A fully-connected neural network (NN) is trained using filtered direct numerical simulation (DNS) data at Re_h =5100 based on the step height. The input to the network is either the strain rate tensor (NN1) or the velocity gradient tensor (NN2), and the output is the SGS stress tensor. In a priori test, the NN-based SGS models predict the SGS stress and dissipation near the shear layer more accurately than traditional models. LES conducted at the same Re_h and on the same grid distribution as those of training data shows accurate predictions of the mean velocity and rms velocity fluctuations in both the shear layer and recirculating region. For the mean dividing streamline, the NN1 shows the best agreement with that of DNS among models considered, and the reattachment lengths (X_r) from NN1 and NN2 are X_r/h = 5.96 and 6.21, respectively, where X_r/h = 6±0.15 from a previous experiment. For LES on coarser grid resolution than that of training data, both NN1 and NN2 still predict X_r well, providing X_r/h = 6.18 and 5.97, respectively, whereas the traditional model underpredicts it (X_r/h = 5.68). The SGS model trained at Re_h =5100 is also applied to higher Reynolds numbers (Re_h = 24000 and 28000) and shows excellent agreements with experimental data for the mean velocity and rms velocity fluctuations.