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 () and power‐law indices () 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.