Inserting machine-learned virtual wall velocity for large-eddy simulation of turbulent channel flows

Abstract

We propose a supervised-machine-learning-based wall model for coarse-grid wall-resolved largeeddy simulation (LES). Our consideration is made on LES of turbulent channel flows with a first grid point set relatively far from the wall (∼ 10 wall units), while still resolving the near-wall region, to present a new path to save the computational cost. Convolutional neural network (CNN) is utilized to estimate a virtual wall-surface velocity from x − z sectional fields near the wall, whose training data are generated by a direct numerical simulation (DNS) at Re τ = 180. The virtual wall-surface velocity is prepared with the extrapolation of the DNS data near the wall. This idea enables us to give a proper wall condition to correct a velocity gradient near the wall. The estimation ability of the model from near wall information is first investigated as a priori test. The estimated velocity fields by the present CNN model are in statistical agreement with the reference DNS data. The model trained in a priori test is then combined with the LES as a posteriori test. We find that the LES can successfully be augmented using the present model at both the friction Reynolds number Re τ = 180 used for training and the unseen Reynolds number Re τ = 360 even when the first grid point is located at 5 wall units off the wall. We also investigate the robustness of the present model for the choice of sub-grid scale model and the possibility of transfer learning in a local domain. The observations through the paper suggest that the present model is a promising tool for recovering the accuracy of LES with a coarse grid near the wall.

Enhancing Computational Fluid Dynamics with Machine Learning

“…This may also be accomplished via transfer functions in spectral space [104], convolutional neural networks [4], or modelling the temporal dynamics of the near-wall region via deep neural networks [78]. Another promising approach based on deep learning was tested in channel flow by Moriya et al [83]. Defining off-wall boundary conditions with machine learning is a challenging yet promising area of research.…”

Log-law recovery through reinforcement-learning wall model for large-eddy simulation

“…The everincreasing availability of high-fidelity simulation data [46][47][48] have motivated the use of machine-learning wall models (MLWMs). The past few years have seen the development of a number of ML WMs 5,20,[49][50][51][52][53][54][55][56][57] . Yang et al 5 was the first to apply ML in WM using supervised MLWM trained at Re τ = 1000 to predict the wall-shear stress.…”

Predicting the wall-shear stress and wall pressure through convolutional neural networks

“…Although the a priori tests showed good results, a posteriori tests did not provide accurate results. Whereas towards defining an off-wall boundary condition, the works like Moriya et al (2021) and Bae and Koumoutsakos (2022) have exhibited promising potential of deep-learning and reinforcement learning based approaches in predicting the flow close to the wall. A survey of machine-learning-based wall models for large-eddy simulations can be found in Vadrot et al (2022).…”