Reconstructing turbulent velocity information for arbitrarily gappy flow fields using the deep convolutional neural network

Abstract

Detailed and reliable flow information is the basis for understanding and further mediating turbulent flows. Due to experimental limitations, such as the absence of seeding particles owing to an inhomogeneous tracer distribution or obstructed optical paths, gappy flow-field data frequently appear with diverse shapes. To resolve this problem, we propose herein the use of a convolutional neural network (CNN) model to reconstruct the velocity field with the missing information of wall-confined turbulent flows. We consider the example of a turbulent channel flow with a frictional Reynolds number Reτ=180 and use machine learning to attain the given objective. High-fidelity numerical data obtained by direct numerical simulation based on the lattice Boltzmann equation are used to generate the datasets required for network training, where data in randomly located square or rectangular regions are masked to provide a maximally realistic instantaneous gappy flow field. The results show that the missing information in gappy regions can be effectively reconstructed for both instantaneous and temporally continuous flow fields. Furthermore, the results are insensitive to the missing locations, even if the locations vary with time. The L2 relative error of the reconstructed instantaneous flow field is generally around 2%. Furthermore, an analysis based on the kinetic-energy spectrum and proper orthogonal decomposition verifies that the reconstructed data are physically consistent with the ground truth. The extracted dominating modes have a maximum relative error level of 10−3. The results obtained herein verify that the proposed CNN model provides complete and reliable data for gappy flows and are physically consistent with physical data.