Large eddy simulation of turbulent flow over a backward-facing step with a neural-network-based subgrid-scale model

A neural-network-based large eddy simulation (LES) is conducted for turbulent flow over a backward-facing step. A fully connected neural network (NN) is trained using filtered direct numerical simulation (DNS) data at the Reynolds number of Reh=5100 based on the free-stream velocity and step height, to develop an NN-based subgrid-scale (SGS) model. Three sets of input variables are considered for training. NN1 is based solely on the filtered strain-rate tensor. NN2 employs the same tensor scaled by the eddy viscosity introduced in the Vreman model, which accounts for the local velocity gradients and grid anisotropy. NN3 further augments the NN2 input with the Leonard stress from the scale-similarity approach. The output of NNs is the SGS stress tensor. For a priori tests, all the NNs show better predictions of the SGS stress and SGS dissipation than the dynamic Smagorinsky model. A posteriori tests (i.e., LES) conducted at the trained Reynolds number and grid distribution show accurate predictions of the reattachment length, mean velocity, and root-mean-square velocity fluctuations. Furthermore, NN2 and NN3 demonstrate good performances on unseen coarser grid resolutions, but NN1 does not. Especially, NN2 maintains predictive capability even at a higher Reynolds number (Reh=28000), whereas NN3 requires ad hoc clipping on negative SGS dissipation for a stable LES at this Reynolds number.