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

• A D2Q8 MRT-LB model is proposed for simulating incompressible porous flows at the REV scale.
• The generalized non-Darcy model is employed to describe the momentum transfer in porous media.
• The generalized Navier–Stokes equations can be recovered through the Chapman–Enskog analysis in the moment space.
• The MRT-LB model is demonstrated by numerical simulations of several typical two-dimensional porous flows.

In this paper, a two-dimensional eight-velocity 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 model. In the model, the porosity is included into the pressure-based equilibrium moments, and the linear and nonlinear drag forces of the porous matrix 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 incompressible generalized Navier–Stokes equations can be recovered. Numerical simulations of several typical porous flows are carried out to validate the present MRT-LB model. It is found that the present numerical results agree well with the analytical solutions and/or other numerical results reported in the literature.