Evaluation of Three Lattice Boltzmann Models for Particulate Flows (Communications in Computational Physics, 2013)
A comparative study is conducted to evaluate three types of lattice Boltzmann equation (LBE) models for fluid flows with finite-sized particles, including thelattice Bhatnagar-Gross-Krook (BGK) model, the model proposed by Ladd [Ladd AJC,J. Fluid Mech., 271, 285-310 (1994); Ladd AJC, J. Fluid Mech., 271, 311-339 (1994)], andthe multiple-relaxation-time (MRT) model. The sedimentation of a circular particle ina two-dimensional infinite channel under gravity is used as the first test problem. Thenumerical results of the three LBE schemes are compared with the theoretical resultsand existing data. It is found that all of the three LBE schemes yield reasonable results in general, although the BGK scheme and Ladd's scheme give some deviationsin some cases. Our results also show that the MRT scheme can achieve a better numerical stability than the other two schemes. Regarding the computational efficiency,it is found that the BGK scheme is the most superior one, while the other two schemesare nearly identical. We also observe that the MRT scheme can unequivocally reducethe viscosity dependence of the wall correction factor in the simulations, which revealsthe superior robustness of the MRT scheme. The superiority of the MRT scheme overthe other two schemes is also confirmed by the simulation of the sedimentation of anelliptical particle.