Extracting fundamental parameters of 2D natural thermal convection using convolutional neural networks

Abstract

The Lattice Boltzmann Method (LBM) is an approach for modeling mesoscopic fluid flow and heat transfer, based on modeling distributions of particles moving and colliding on a lattice. Using a perturbative formulation of the Boltzmann equation, it scales to the macroscopic Navier–Stokes equation. We simulate natural thermal convection via LBM in a 2D rectangular box being heated from below and cooled from above, and use the results as training, testing, and generalization datasets to build a deep learning model. GoogLeNet, a convolutional neural network, is used to classify the simulation results based on two parameters: Rayleigh (Ra) and Prandtl (Pr) numbers, from a single snapshot of either the entire modeling field of resolution 1024×1024, or a 224×224 crop. For each fixed Pr in a range from 1 to 128, increasing by a factor of 2, we estimate Ra with an accuracy varying from 40% to 90%, depending on the chosen augmentation strategy. For each fixed Ra in the range from 105 to 109, increasing of a factor 10, the method predicts Pr with a systematically lower accuracy ranging from 30% to 80%. This approach has great potential for industrial applications like being able to control the industrial flow or scientific research on geophysical ones including the transport of heat in the earth’s interiors, ocean, and atmosphere.