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.