A Multiple-Relaxation-Time Lattice Boltzmann Model for Natural Convection in a Hydrodynamically and Thermally Anisotropic Porous Medium under Local Thermal Non-Equilibrium Conditions

To investigate the natural convective process in a hydrodynamically and thermally anisotropic porous medium at the representative elementary volume (REV) scale, the present work presented a multiple-relaxation-time lattice Boltzmann method (MRT-LBM) based on the assumption of local thermal non-equilibrium conditions (LTNE). Three sets of distribution function were used to solve the coupled momentum and heat transfer equations. One set was used to compute the flow field based on the generalized non-Darcy model; the other two sets were used to solve the temperature fields of fluid and solid under the LTNE. To describe the anisotropy of flow field of the porous media, a permeability tensor and a Forchheimer coefficient tensor were introduced into the model. Additionally, a heat conductivity tensor and a special relaxation matrix with some off-diagonal elements were selected for the thermal anisotropy. Furthermore, by selecting an appropriate equilibrium moments and discrete source terms accounting for the local thermal non-equilibrium effect, as well as choosing an off-diagonal relaxation matrix with some specific elements, the presented model can recover the exact governing equations for natural convection under LTNE with anisotropic permeability and thermal conductivity with no deviation terms through the Chapman-Enskog procedure. Finally, the proposed model was adopted to simulate several benchmark problems. Good agreements with results in the available literatures can be achieved, which indicate the wide practicability and the good accuracy of the present model.