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Three-dimensional multiple-relaxation-time lattice Boltzmann model for convection heat transfer in porous media at the REV scale

In this paper, a three-dimensional (3D) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is presented for convection heat transfer in porous media at the representative elementary volume (REV) scale. The model is developed in the framework of the double-distribution-function (DDF) approach: an MRT-LB model of the density distribution function with the D3Q19 lattice (or D3Q15 lattice) is proposed to simulate the flow field based on the generalized non-Darcy model, while an MRT-LB model of the temperature distribution function with the D3Q7 lattice is proposed to simulate the temperature filed. The present model is employed to simulate mixed convection flow in a porous channel and natural convection in a cubical porous cavity. The numerical results demonstrate the effectiveness and accuracy of the present model in solving 3D convection heat transfer problems in porous media. The numerical results also demonstrate that the present model is approximately second-order accuracy in space. In addition, an enthalpy-based DDF-MRT model for 3D solid-liquid phase change with convection heat transfer in porous media is also presented.