A Localized Mass-Conserving Lattice Boltzmann Approach for Non-Newtonian Fluid Flows (Communications in Computational Physics, 2018)
A mass-conserving lattice Boltzmann model based on the Bhatnagar-Gross-Krook(BGK) model is proposed for non-Newtonian fluid flows. The equilibrium distributionfunction includes the local shear rate related with the viscosity and a variableparameter changing with the shear rate. With the additional parameter, the relaxationtime in the collision can be fixed invariable to the viscosity. Through the Chapman-Enskoganalysis, the macroscopic equations can be recovered from the present mass-conservingmodel. Two flow problems are simulated to validate the present modelwith a local computing scheme for the shear rate, and good agreement with analyticalsolutions and/or other published results are obtained. The results also indicate thatthe present modified model is more applicable to practical non-Newtonian fluid flowsowing to its better accuracy and more robustness than previous methods.