Three-dimensional D3Q27 multiple-relaxation-time lattice Boltzmann simulation of Herschel–Bulkley viscoelastic fluids in a cubic cavity with top lid driven diagonally

Abstract

Graphics Processing Unit (GPU) accelerated multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) is used for the simulation of Herschel–Bulkley non-Newtonian fluids in a three-dimensional (3D) cubic cavity with the top lid-driven diagonally. For the 3D simulation, a D3Q27 lattices model, which is more stable and well-accepted in the LBM community, is used in the present MRT-LBM. Simulations using numerical models are run for a variety of dimensionless variables, including the Reynolds numbers ($Re=300,600,1000,1200$), Bingham number ($Bn=0.0,0.5,1.0,2.0$), Power-law index, ($n=0.8$). In the present numerical simulation, the GPU has used a parallel computing technique based on the Compute Unified Device Architecture (CUDA) C++ programming. MRT-LBM code is validated for the Newtonian and non-Newtonian power law fluid with a lid-driven cubic cavity. The numerical results obtained regarding the streamlines, velocity, viscosity distributions, and the iso-surfaces of the non-Newtonian viscosity are presented. The current numerical findings could potentially function as benchmark results for validating 3D codes validation for the non-Newtonian fluids.