“…Numerical simulation of fluid flow and mass transport in deforming porous media has received a considerable attention and has been the subject of many investigations in recent years (Thomas et al, 1980;Lewis et al, 1975Lewis et al, , 1986Lewis et al, , 1991aLewis and Garner, 1972;Lewis and Tran, 1989;Lewis and Sukirman, 1993;Sukirman and Lewis, 1993;Lewis and Ghafouri, 1993;Ghafouri and Lewis, 1996;Rahman and Lewis, 1999;Pao et al, 2001;Masters et al, 2000;Pao and Lewis, 2002;Masad et al, 2002;Gutierrez and Lewis, 2002;Lewis and Pao, 2002;Wang et al, 2003). This interest is primarily due to the fact that this kind of structure is encountered in many engineering applications such as drying processes, filtration, thermal insulation, geothermal systems, ground water and oil flow, as well as compact heat exchangers (Guerroudj and Kahalerras, 2012).…”