An evaluation of lattice Boltzmann equation methods for simulating flow through porous media

Abstract

We evaluated lattice Boltzmann equation (LBE) methods for modeling flow through porous media. We compared a three-dimensional, 19-velocity, multiple-relaxation-time (MRT) LBE model with a popular single-relaxation-time, Bhatnagar-Gross-Krook (BGK) LBE model. It can be shown that the latter (BGK-LBE) model is a special case of the former (MRT-LBE) model for a certain set of parameter constraints used in the collision operator. We compared the accuracy of the two models for two test cases: (1) Poiseuille flow between parallel plates, and (2) flow past a periodic simple cubic (SC) array of spheres. We also compared two solid-phase, boundary condition approximations: (1) a linearly interpolated bounce-back (LIBB) method, and (2) a standard bounce-back (SBB) method without interpolation. Our results clearly demonstrate advantages of the MRT-LBE model over its BGK counterpart, and the benefits of the LIBB method over the SBB method in terms of numerical accuracy.