Nonlinear flow in porous media

Abstract

The flow of an incompressible liquid at nonzero Reynolds number Re in a two-dimensional model porous medium is studied via numerical simulation. The geometry is a random array of cylinders of square cross section and spectral element methods are used. We find a transition from linear Darcy flow at vanishing Re, to a cubic transitional regime at low Re, and then a quadratic Forchheimer when $\mathrm{Re}=O(1).$ In addition, some general remarks on scaling behavior and the form of the flow equation at finite Re are presented.