A comparative study on the lattice Boltzmann models for predicting effective diffusivity of porous media

Abstract

In this paper, we present a comparative study on the popular single-relaxation-time lattice Boltzmann (LB) model (also called BGK model) and multiple-relaxation-time (MRT) LB model for calculating effective diffusivity of porous media with non-permeable inclusions. Through performing some simulations of the diffusion in simple porous media composed of cylinders in a square or staggered arrangement, we find that the predicted effective diffusivity based on the BGK model is dependent on the relaxation parameter, which is an artificial result in the framework of LB method. In the MRT model, however, this artificial result inherent in the BGK model can be eliminated through tuning one of the free relaxation parameters. The results in this work also demonstrate that the MRT model is more suitable than the BGK model in the study of diffusion in porous media and prediction of effective diffusivity.