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ISSN Druckformat: 1091-028X
ISSN Online: 1934-0508
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Darcy's Law for a Heterogeneous Porous Medium
ABSTRAKT
We consider slow viscous flow of a Newtonian fluid through a spatially varying porous medium. Applying the method of homogenization in a heterogeneous porous medium constructed by a microscopic, locally periodic structure we are able to derive an appropriate form of Darcy's law. This is a macroscopic relationship between the average fluid velocity and the overall pressure and external force mediated by a heterogeneous permeability tensor. A simple explicit example, which is amenable to analytical resolution and which exhibits part of the complexity of a general situation, is considered.
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