建立了倾斜多孔方腔自然对流的非正交多松弛系数格子 Boltzmann (MRT-LB)模型，选取典型热流动问题分析了非正交转换矩阵的 MRT-LB 模型数值稳定性和运算效率，并对倾斜多孔方腔内自然对流现象进行了模拟研究，讨论了孔隙度 ε(ε = 0. 4，0. 6，0. 9)、倾角 θ ( －180°≤θ≤180°)、Rayleigh 数(10⁴ ≤Ra≤10⁷ )及 Darcy 数(Da = 10^-4，10^-2)等参数对流动传热的影响． 结果表明:非正交转换矩阵的 MRT-LB 模型具有更好的数值稳定性和收敛速度;倾斜多孔方腔高温壁面上平均 Nusselt 数随倾角变化呈 M 型分布;Ra 数、Da 数增大使得 Nusselt 数最大值所对应的倾斜角度 θ max 呈滞后规律;低 Ra 数时Nusselt 数曲线出现不连续变化现象． 最后通过曲线拟合得到 Nusselt 数与Ra^* (Ra^* =DaRa)数的幂函数关系式．

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．