Abstract
To obtain the effective parameters of a heterogeneous medium from the microscale description, one has to solve a boundary value problem defined on a representative cell. For practical purposes, the medium is often considered as periodic and the period represents the representative cell. In some cases the cell posesses plane symmetries. The aim of this note is to investigate the simplifications that are introduced by such symmetries. The case of diffusion in a composite or porous medium, and the case of a Darcy flow in a porous medium are investigated. The consequences of plane symmetry on the condition of scale separation are addressed. It is shown that the scale separation condition does not always has to be fulfilled to determine effective parameters from experiments.
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Auriault, JL., Lewandowska, J. Upscaling: Cell Symmetries and Scale Separation. Transport in Porous Media 43, 473–485 (2001). https://doi.org/10.1023/A:1010734421457
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DOI: https://doi.org/10.1023/A:1010734421457