GPU-Accelerated Lattice Boltzmann Simulations of Power-Law Non-Newtonian Fluid Flow in a Diagonally Driven Cavity Using D3Q27 MRT-LBM

Abstract

The study examines the flow dynamics of power-law non-Newtonian fluids in a cubic cavity with a top lid-driven diagonally-driven diagonally using the D3Q27 multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). This situation frequently occurs in both natural and industrial processes. Utilizing CUDA C++ programming on a graphics processing unit (GPU) speeds up the simulations, enabling effective investigation of intricate fluid dynamics. Non-Newtonian behaviors, such as shear-thinning and shear-thickening properties, are frequently found in many real-world fluid systems and are captured by the power-law rheology model. LBM provides a mesoscopic method that makes handling intricate geometries easier and scales effectively on GPUs and other parallel computing architectures. The simulations investigate how Reynolds numbers ($Re=100,200,400,500,600,800,1000,1200$) and power-law indices ($n=0.8,1,1.4$) affect non-Newtonian fluid flow characteristics like streamlines, velocity profiles, viscosity distributions, iso-surfaces, and helicity (twistiness). GPU acceleration makes faster simulations and parametric research possible, improving computational efficiency. These findings provide information for non-Newtonian fluid engineering applications in the food industry, biomedical engineering, and polymer processing. Because of their decreased viscosity, shear-thinning fluids have higher helicity than shear-thickening fluids. The numerical results of the study offer applicable standards for evaluating 3D codes for fluids with non-Newtonian power laws. The uniqueness is that a D3Q27 multiple-relaxation-time lattice Boltzmann method (MRT-LBM) framework with GPU acceleration can be used to model an underexplored situation, revealing fluid dynamics and rheological features with unprecedented detail and computing efficiency. We also examine how the power-law index influences vortex generation, helicity, and flow stability in a diagonally driven cavity. Additionally, a comparison of the D3Q19 and D3Q27 MRT-LBM models is provided, emphasizing how they handle complex fluid behaviors differently.