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

Abstract

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.

Large eddy simulation of flow over a circular cylinder with a neural-network-based subgrid-scale model

“…Most of the previous studies have adopted simple NN architectures having consecutive layers with multiple nodes (see, for example, Sarghini, de Felice & Santini 2003;Wollblad & Davidson 2008;Gamahara & Hattori 2017;Pal 2019;Xie et al 2020a,b,c;Yuan et al 2020;Park & Choi 2021;Stoffer et al 2021;Subel et al 2021;Wang et al 2021;Kang et al 2023), as shown in figure 5(a). Park & Choi (2021) used an NN with two hidden layers and 128 nodes per hidden layer by setting Sij or ᾱij as the input and τ ij as the output, respectively, and showed its better performance than that of DSM for turbulent channel flow.…”

Wavelet Transforms and Machine Learning Methods for the Study of Turbulence

“…The linear combination of the Leonard (resolved) stress (τ L ij ) with the subgrid-scale stress (τ ij ) improves the prediction of the true subfilter-scale stress (τ s ij ). Note that Kang et al [100] proposed a mixed-subgrid-scale model using the NN approach and tested the performance by simulating isotropic turbulence and turbulent channel flow. Within the scope of the present review, we find that the underlying premise of considering the POD method in LES is that the low-dimensional POD of short-time snapshots also attenuates the small-scale fluctuations by time-domain filtering (see [89]).…”