A multiple-relaxation-time lattice Boltzmann model for convection heat transfer in porous media

In this paper, a two-dimensional (2D) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating convection heat transfer in porous media at the representative elementary volume scale. In the model, a D2Q9 MRT-LB equation is adopted to simulate the flow field, while a D2Q5 MRT-LB equation is employed to simulate the temperature field. The generalized model is employed to model the momentum transfer, and the effect of the porous media is considered by introducing the porosity into the equilibrium moments, and adding a forcing term to the MRT-LB equation of the flow field in the moment space. The present MRT-LB model is validated by numerical simulations of several 2D convection problems in porous media. The present numerical results are in excellent agreement with the analytical solutions and/or the well-documented data reported in previous studies. It is also found that the present MRT-LB model shows better numerical stability than the LBGK model.