Abstract This work deals with CFD modeling method under Fortran 90 with dimensionless setting. A numerical study of flow and heat transfer inside a cylinder partially filled with a porous material and with two pistons is provided during compression stroke. Phase shift between the two pistons is about π/2. Air inside cylinder is considered as Newtonian perfect gas. The flow is supposed to be laminar and steady. The Brinkman-Forcheimer Lapwood theory is adopted to simulate transfer momentum in the porous media. Dimensional governing equations are solved using control volume with finite element method (MVCEF). The obtained results are in good agreement with literature numerical investigations. The effect of the porous media properties (length and porosity) and heat transfer on flow was investigated. Results show that the optimum heat convective flux is achieved for a porosity of 0.9 and a permeability of 0.7. Results show a close relationship between geometry parameters of the regenerator and the pressure drop. An optimum value of regenerator length is expected for each working condition.