Neural-network-based mixed subgrid-scale model for turbulent flow

An artificial neural-network-based subgrid-scale (SGS) model, which is capable of predicting turbulent flows at untrained Reynolds numbers and on untrained grid resolution is developed. Providing the grid-scale strain-rate tensor alone as an input leads the model to predict a SGS stress tensor that aligns with the strain-rate tensor, and the model performs similarly to the dynamic Smagorinsky model. On the other hand, providing the resolved stress tensor as an input in addition to the strain-rate tensor is found to significantly improve the prediction of the SGS stress and dissipation, and thereby the accuracy and stability of the solution. In an attempt to apply the neural-network-based model trained for turbulent flows with a limited range of the Reynolds number and grid resolution to turbulent flows at untrained conditions on untrained grid resolution, special attention is given to the normalisation of the input and output tensors. It is found that the successful generalization of the model to turbulence for various untrained conditions and resolution is possible if distributions of the normalised inputs and outputs of the neural network remain unchanged as the Reynolds number and grid resolution vary. In a posteriori tests of the forced and the decaying homogeneous isotropic turbulence and turbulent channel flows, the developed neural-network model is found to predict turbulence statistics more accurately, maintain the numerical stability without ad hoc stabilisation such as clipping of the excessive backscatter, and to be computationally more efficient than the algebraic dynamic SGS models.