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Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

Davit, Yohan and Bell, Christopher G. and Byrne, Helen and Chapman, Lloyd A. C. and Kimpton, Laura S. and Lang, Georgina E. and Leonard, Katherine H. L. and Oliver, James M. and Pearson, Natalie C. and Shipley, Rebecca J. and Waters, Sarah L. and Whiteley, Jonathan P. and Wood, Brian D. and Quintard, Michel Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare? (2013) Advances in Water Resources, 62 (part B). 178-206. ISSN 0309-1708

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Official URL: http://dx.doi.org/10.1016/j.advwatres.2013.09.006

Abstract

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.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Advances in Water Resources website : http://www.sciencedirect.com/science/journal/03091708
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > University College of London - UCL (UNITED KINGDOM)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Oregon State University (USA)
Other partners > University of Oxford (UNITED KINGDOM)
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Deposited On:24 Mar 2014 14:28

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