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 large-eddy simulation (LES). Our consideration is made on LES of turbulent channel flows with a first grid point set relatively far from the wall ($\sim$ 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 ${\mathrm{Re}}_{\tau }=180$. 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 ${\mathrm{Re}}_{\tau }=180$ used for training and the unseen Reynolds number ${\mathrm{Re}}_{\tau }=360$ 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.

arXiv comment18 pages, 14 figures

References in corpus (14)

• Adam: A Method for Stochastic Optimization
• Turbulence Modeling in the Age of Data
• Super-resolution reconstruction of turbulent flows with machine learning
• Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
• Deep Neural Networks for Data-Driven Turbulence Models
• Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning
• Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow
• Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data
• Probabilistic neural networks for fluid flow surrogate modeling and data recovery
• Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low-dimensionalization
• Sub-grid scale model classification and blending through deep learning
• Reservoir computing model of two-dimensional turbulent convection
• Turbulent scalar flux in inclined jets in crossflow: counter gradient transport and deep learning modelling
• Convolutional-network models to predict wall-bounded turbulence from wall quantities

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