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

Yohan Davit; Christopher G. Bell; Helen M. Byrne; Lloyd A.C. Chapman; Laura S. Kimpton; Georgina E. Lang; Katherine H.L. Leonard; James M. Oliver; Natalie C. Pearson; Rebecca J. Shipley; Sarah L. Waters; Jonathan P. Whiteley; Brian D. Wood; Michel Quintard

doi:10.1016/j.advwatres.2013.09.006

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

Yohan Davit, Christopher G. Bell, Helen M. Byrne, Lloyd A.C. Chapman, Laura S. Kimpton, Georgina E. Lang, Katherine H.L. Leonard, James M. Oliver, Natalie C. Pearson, Rebecca J. Shipley, Sarah L. Waters, Jonathan P. Whiteley, Brian D. Wood, Michel Quintard

Research output: Contribution to journal › Article › peer-review

128 Scopus citations

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. © 2013 Elsevier Ltd.

Original language	English (US)
Pages (from-to)	178-206
Number of pages	29
Journal	Advances in Water Resources
Volume	62
DOIs	https://doi.org/10.1016/j.advwatres.2013.09.006
State	Published - Dec 2013
Externally published	Yes

Bibliographical note

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.

Access to Document

10.1016/j.advwatres.2013.09.006

Cite this

Davit, Y., Bell, C. G., Byrne, H. M., Chapman, L. A. C., Kimpton, L. S., Lang, G. E., Leonard, K. H. L., Oliver, J. M., Pearson, N. C., Shipley, R. J., Waters, S. L., Whiteley, J. P., Wood, B. D., & Quintard, M. (2013). Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare? Advances in Water Resources, 62, 178-206. https://doi.org/10.1016/j.advwatres.2013.09.006

@article{7f3586d816214dc0a0f324418326510a,

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

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. {\textcopyright} 2013 Elsevier Ltd.",

author = "Yohan Davit and Bell, {Christopher G.} and Byrne, {Helen M.} 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 Michel Quintard",

note = "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.",

year = "2013",

month = dec,

doi = "10.1016/j.advwatres.2013.09.006",

language = "English (US)",

volume = "62",

pages = "178--206",

journal = "Advances in Water Resources",

issn = "0309-1708",