Cascaded lattice Boltzmann modeling and simulations of three-dimensional non-Newtonian fluid flows

Non-Newtonian fluid flows, especially in three dimensions (3D), arise numerous settings of interest to physics. Prior studies using the lattice Boltzmann method (LBM) such flows have so far been limited mainly two and used less robust collision models. In this paper, we develop a new 3D cascaded LBM based on central moments multiple relaxation times (MRT) three-dimensional, nineteen velocity (D3Q19) for simulation generalized Newtonian (power law) flows. The second order are varied locally local shear rate parameterized by consistency coefficient power law index nonlinear constitutive relation fluid. Numerical validation study various benchmark problems, including complex non-Newtonian flow cubic cavity at different Reynolds numbers magnitudes encompassing thinning thickening fluids, presented. Furthermore, demonstrate advantages proposed moments, numerical stability comparisons against LBMs single time model MRT raw made. results accuracy, grid convergence significant improvements fluids.