多孔介质中单相气体局部流动的均质化建模OA北大核心CSTPCD

The application of asymptotic homogenization method was investigated based on the filtration theory for single-phase gas,and the mathematical model and numerical method for the gas flow at the pore scale were developed.With the asymptotic homogenization method,a local problem of periodic cells was established to de-scribe the local flow process of a single-phase gas at the pore scale of the periodic porous medium.The special mathematical properties and physical significance of the local problem were discussed.With a simplified ap-proach based on symmetric and antisymmetric extensions,a least squares finite element method for the local problem was proposed,to overcome the numerical difficulties due to averaging operators and periodic boundary conditions.The solution of the local problem was obtained with accurate local velocity and pressure distribu-tions in a single pore,and with gas permeability evaluation of porous media only in knowledge of the pore ge-ometry.Beyond the local problem,the analytical solution of the Poiseuille flow in microtubes was obtained through theoretical analysis,to verify the proposed mathematical model and the numerical algorithm.Finally,a 3D periodic porous structure was considered,and numerical results of local flow in a single pore and permea-bility coefficients in porous media were obtained.