Abstract: A non-orthogonal multiple-relaxation-time lattice Boltzmann model is developed for simulating convection heat transfer in an inclined cavity filed with porous media at a representative elementary volume scale． The numeri-cal stability and computational efficiency of the Bhatnagar-Gross-Krook (BGK) model and the multiple relaxation model (MRT) are analyzed and compared by means of selecting the typical flow and heat transfer problems． It's found that present numerical results are well congruous with the previous results． Then simulation is performed in the convective heat transfer in inclined cavity，and the influence of porosity ε (ε =0. 4，0. 6，0. 9)，Darcy num-ber (Da =10^-4 ，10^-2 )，Ｒayleigh number (10⁴ ≤Ra≤10⁷) and inclined angle θ ( －180°≤θ≤180°) is dis-cussed on the convective heat transfer． The results indicate that the non-orthogonal MRT-LB model has good numeri-cal stability and convergence speed when low viscosity is dealt with． Average Nusselt number at hot sidewall pre-sents the symmetrical distribution of M type with the change of inclined angle and obtains the extreme value in the specific inclination interval． With the Darcy number，Rayleigh number increasing，the maximum average Nusselt number corresponding angle presents hysteresis phenomenon． The average Nusselt number discontinues change at low Ra number． The power function relation of the average Nusselt number with Ra^* number (Ra^* = DaRa) is obtained．

Key words: multiple-relaxation-time lattice, Boltzmann model, inclined porous square cavity, natural convection, numerical stability