On Machine-Learning-Aided Two-Scale Solution for Turbulent Fluid Flows

Abstract

Scale-resolving solutions for computational fluid dynamics problems have usually been challenging due to their request for computing resources. A two-scale framework was proposed for more efficient solutions to couple a local fine-mesh solution with a global coarse-mesh solution. The methodology was successfully implemented and demonstrated for a canonical turbulent channel flow and for a tripped turbulent boundary layer. The solution mapping from the local fine-mesh to the global coarse-mesh region is realized by modifying the flow-governing equations in the under-resolved coarse-mesh region through adding extra forcing source terms generated from the space–time-averaged fine-mesh solutions. However, the high-gradient transitional region presents additional challenges when applying the Chebyshev spectral method for mapping the source terms; thus the high-gradient frontal region has not been fully resolved in the streamwise direction. In the present work, the propagation of the source terms is facilitated by machine learning tools (multilayer perceptron-based neural network) so as to implement the method in flowfields with high gradients or drastic changes in the mean velocity. The neural-network-based propagation model is shown to be capable of accurately estimating the source terms in the near-wall coarse-mesh region. The mean flow there thus can be nicely reproduced by the source-term propagation. The machine-learning tools thus provide potential as the more advanced source-term propagation method for the two-scale framework to be implemented in more complicated flowfields.