Porous media flows belong to the general class of creeping flows, those with very small velocities. There is a wide variety of significant engineering, ecological and geological applications that require an understanding of flow through porous media. Some examples include flow in confined and unconfined aquifers, groundwater contamination, saltwater intrusion, management of well-field withdrawal or recharge rates, and so forth. Most of the groundwater phenomena can be described by partial differential equations mainly of the parabolic or elliptic type, along with the appropriate boundary and initial conditions (Bear and Verruijt 1987).