Extracting Fundamental Parameters of 2-D Natural Thermal Convection Using Convolutional Neural Networks*

The Lattice Boltzmann Method (LBM) is an approach for modelling mesoscopic fluid flow and heat transfer, based on modelling distributions of particles moving and colliding on a lattice. Based on a perturbative formulation of the Boltzmann Equation, it scales to the macroscopic Navier Stokes equation[1]. We simulate natural thermal convection via LBM in a 2-D rectangular box being heated from below, cooled from above[2], and use the results as training, testing and generalization datasets to build a deep learning model. GoogLeNet, a convolutional neural network (CNN)[3], is used to classify the simulation results based on two parameters: Rayleigh (Ra) and the Prandtl (Pr) numbers. For each fixed Pr from 1 to 128, we extract Ra with accuracy around 90% from a single snapshot. For a fixed Ra, the classification of Pr shows greater uncertainties. Finally, we test the method performance from small randomly placed snapshots of a larger convecting domain. This approach has a great potential for industrial application like electronic equipment cooling or scientific research on Earth and in Space.

References

[1] Sharma, K. V., Straka, R., & Tavares, F. W. (2020). Current status of Lattice Boltzmann Methods applied to aerodynamic, aeroacoustic, and thermal flows. Progress in Aerospace Sciences, 115, 100616.

[2] Mora, Peter, Gabriele Morra, and David A. Yuen. "A concise python implementation of the lattice Boltzmann method on HPC for geo-fluid flow." Geophysical Journal International 220.1 (2020): 682-702.

[3] Szegedy, Christian, et al. "Going deeper with convolutions." Proceedings of the IEEE conference on computer vision and pattern recognition. 2015.