TY - JOUR
T1 - Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?
AU - Davit, Yohan
AU - Bell, Christopher G.
AU - Byrne, Helen M.
AU - Chapman, Lloyd A.C.
AU - Kimpton, Laura S.
AU - Lang, Georgina E.
AU - Leonard, Katherine H.L.
AU - Oliver, James M.
AU - Pearson, Natalie C.
AU - Shipley, Rebecca J.
AU - Waters, Sarah L.
AU - Whiteley, Jonathan P.
AU - Wood, Brian D.
AU - Quintard, Michel
N1 - KAUST 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.
PY - 2013/12
Y1 - 2013/12
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/598515
UR - https://linkinghub.elsevier.com/retrieve/pii/S0309170813001589
UR - http://www.scopus.com/inward/record.url?scp=84888286643&partnerID=8YFLogxK
U2 - 10.1016/j.advwatres.2013.09.006
DO - 10.1016/j.advwatres.2013.09.006
M3 - Article
SN - 0309-1708
VL - 62
SP - 178
EP - 206
JO - Advances in Water Resources
JF - Advances in Water Resources
ER -