Mesoscopic CUDA 3D MRT-LBM Simulation of Natural Convection of Power-Law Fluids in a Differentially Heated Cubic Cavity with a Machine Learning Cross-Validation

The aim of this study was to investigate the natural convection of power-law fluids in a differentially heated cubic cavity by considering graphics process unit (GPU)-accelerated mesoscopic multiple-relaxation-time (MRT)-lattice Boltzmann method (LBM). The Compute Unified Device Architecture (CUDA) C programming language was implemented for a robust workflow to obtain accurate and quicker outcomes. The present approach initially follows twofold validations with well-established literature after the grid independence test (GIT). Later, Levenberg-Marquardt (LM) algorithm was applied for the nonlinear surface analyses, followed by the random forest (RF) machine learning method for the cross-validation of CUDA C-obtained results, with coefficient of determination (R-2) obtained between 0.96 and 0.99. In the numerical simulations, different Rayleigh numbers, Ra =(10(4), 10(5), 10(6)), and power-law indices (n = 0.7, 0.8, 1.0, 1.2, 1.4) were integrated to study the heat transfer and entropy production values. The major findings of this study provide evidence that GPU-based simulation can provide robust outcomes and can be validated by a machine learning algorithm in a mesoscopic scale in a complex geometry concurrently with different temperature conditions by considering the LBM-MRT scheme. At the end of the study, it was found that the Ra numbers had significant impacts on the convective heat transfer, particularly at Ra = 10(6) due to the dominance of buoyancy inside the enclosure. Furthermore, the distribution of temperature was more pronounced from the heated wall, particularly at power-law indices, n = 0.7, 1.0, and had a less significant impact at n = 1.4. The power-law fluid represented by n = 0.7 exhibited quantitatively greater peak velocity and temperature as well as the maximum entropy production. One of the promising aspects of this study is that a data-driven approach has been found to be beneficial in the modelling and simulations which can be systematically investigated through CUDA C-obtained outcomes.