Abstract
A porous medium may have a microstructure on a scale much smaller than the macroscopic scale which is of interest. Phenomena arising at the macroscopic levels are described by taking mean values of the microscopic quantities and there are several methods of doing this. In this chapter we are interested in the homogenization method. In fact a more descriptive name for this method is an asymptotic method for the study of periodic media. This means that the method consists of taking the mean value for the periodic structure of the media. Consequently, it is important to note that we must use a periodic model of a porous medium. The major reason for the choice of such a model is that we have at our disposal a good mathematical technique which permits us to prove the existence and the uniqueness of the solution, to construct the macroscopic equation and to define exactly the macroscopic or effective coefficients, etc. By use of this method it is possible to obtain new results concerning different macroscopic equations arising in flow through porous media, to indicate the correct boundary conditions, or to make clearer the dimensionless parameters which are significant in such phenomena.
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Ene, H.I. (2004). Modeling the Flow Through Porous Media. In: Ingham, D.B., Bejan, A., Mamut, E., Pop, I. (eds) Emerging Technologies and Techniques in Porous Media. NATO Science Series, vol 134. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0971-3_3
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DOI: https://doi.org/10.1007/978-94-007-0971-3_3
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