Prediction of wall-bounded turbulence from wall quantities using convolutional neural networks
This work addresses turbulence modeling for fluid dynamics researchers, offering incremental improvements in prediction accuracy and efficiency.
The authors tackled the problem of predicting streamwise velocity fields in turbulent open channel flow from wall-shear-stress inputs using convolutional neural networks, achieving lower error than linear methods in both instantaneous fields and turbulent statistics. They found that using a dataset with higher time-step intervals improved generalization across wall-normal locations, and transfer learning reduced training time by a factor of 4.
A fully-convolutional neural-network model is used to predict the streamwise velocity fields at several wall-normal locations by taking as input the streamwise and spanwise wall-shear-stress planes in a turbulent open channel flow. The training data are generated by performing a direct numerical simulation (DNS) at a friction Reynolds number of $Re_τ=180$. Various networks are trained for predictions at three inner-scaled locations ($y^+ = 15,~30,~50$) and for different time steps between input samples $Δt^{+}_{s}$. The inherent non-linearity of the neural-network model enables a better prediction capability than linear methods, with a lower error in both the instantaneous flow fields and turbulent statistics. Using a dataset with higher $Δt^+_{s}$ improves the generalization at all the considered wall-normal locations, as long as the network capacity is sufficient to generalize over the dataset. The use of a multiple-output network, with parallel dedicated branches for two wall-normal locations, does not provide any improvement over two separated single-output networks, other than a moderate saving in training time. Training time can be effectively reduced, by a factor of 4, via a transfer learning method that initializes the network parameters using the optimized parameters of a previously-trained network.