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Multiple-relaxation-time lattice Boltzmann modeling of incompressible flows in porous media

In this paper, a two-dimensional eight-velocity (D2Q8) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for incompressible porous flows at the representative elementary volume scale based on the Brinkman-Forchheimer-extended Darcy formulation. In the model, the porosity is included into the pressure-based equilibrium moments, and the linear and nonlinear drag forces of the porous media are incorporated into the model by adding a forcing term to the MRT-LB equation in the moment space. Through the Chapman-Enskog analysis, the generalized Navier-Stokes equations can be recovered exactly without artificial compressible errors. Numerical simulations of several typical two-dimensional porous flows are carried out to validate the present MRT-LB model. The numerical results of the present MRT-LB model are in good agreement with the analytical solutions and/or other numerical solutions reported in the literature.