Toward neural-network-based large eddy simulation: application to turbulent channel flow

A fully connected neural network (NN) is used to develop a subgrid-scale (SGS) model mapping the relation between the SGS stresses and filtered flow variables in a turbulent channel flow at Re_τ = 178. A priori and a posteriori tests are performed to investigate its prediction performance. In a priori test, an NN-based SGS model with the input filtered strain rate or velocity gradient tensor at multiple points provides highest correlation coefficients between the predicted and true SGS stresses, and reasonably predicts the backscatter. However, this model provides unstable solution in a posteriori test, unless a special treatment such as backscatter clipping is used. On the other hand, an NN-based SGS model with the input filtered strain rate tensor at single point shows an excellent prediction capability for the mean velocity and Reynolds shear stress in a posteriori test, although it gives low correlation coefficients between the true and predicted SGS stresses in a priori test. This NN-based SGS model trained at Re_τ = 178 is applied to a turbulent channel flow at Re_τ = 723 using the same grid resolution in wall units, providing fairly good agreements of the solutions with the filtered direct numerical simulation (DNS) data. When the grid resolution in wall units is different from that of trained data, this NN-based SGS model does not perform well. This is overcome by training an NN with the datasets having two filters whose sizes are bigger and smaller than the grid size in large eddy simulation (LES). Finally, the limitations of NN-based LES to complex flow are discussed.