Non-linear seepage flow through a rigid porous medium

The non-linear seepage flow through a porous medium is generally described by the Forchheimer law which contains a square velocity term. However, for very small Reynolds numbers, when the seepage law of a fluid through a rigid porous medium was investigated by using the method of homogenization for periodic structures, it was shown that the small non-linear correction to the Darcy law was a cubic term. The aim of the present paper is to extend these results to laminar flows with large Reynolds numbers and to compare them to the Forchheimer law.