A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works. © 2013 Elsevier Ltd.
|Original language||English (US)|
|Number of pages||29|
|Journal||Advances in Water Resources|
|State||Published - Dec 2013|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This work was supported in part by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST). Dr. Wood was supported in part by the U.S. Department of Energy, Office of Science (Subsurface Biogeochemistry Research program through the PNNL Subsurface Science Focus Area), and by NSF Mathematics under Grant 1122699.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.