A micro-macro combined approach is presented for modeling the flow and thermal fields through a porous medium when the cell structure is well defined. This approach entailed modeling regenerators made of stacked welded screens by using a fundamental periodic two-dimensional or three-dimensional cellular unit and solving for the flow and thermal field inside the units. Periodic boundary conditions were set on the boundaries parallel to the stream wise direction, while a pseudo-periodic boundary condition with a prescribed volumetric flow rate was assigned to the inlet and outlet boundaries of the unit cell. The computed pressure drop data of the flow through the cellular unit and the heat transfer rate between solid and fluid were compared against experimental data. Comparisons were made between the micro model CFD results and experimental data for the matrix.