Hydro-kinetic Approach in Non-Newtonian Lattice Boltzmann Flow Simulation

The simulation of non-Newtonian fluid flow is a challenging task both from the theoretical and the numerical points of view. In particular, most of the existing methods are not adequate to solve the strong nonlinear flow problem. It is, therefore, clear that development of new tools are necessary. In this note, we propose the truncated hydro-kinetic (HK) model of Yakhot to simulate non-Newtonian fluids exposed to a strong shear. Although the proposed model is numerically simple, it is capable of generating non-trivial predictions for strong shear flows. The truncated HK model reported here utilizes a shear-rate-dependent relaxation time for a non-Newtonian fluid. For the feasibility study, we examined benchmark flows: The calculated pressure driven channel flow results in our model are in excellent agreement with the Carreau model. In addition, the results from the parametric study of 4:1 sudden contraction flow clearly demonstrate transition regions, and the HK model points towards a shear thinning behavior