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 Re=O(1). In addition, some general remarks on scaling behavior and the form of the flow equation at finite Re are presented.
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Rojas et al. (1998) studied this question.
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