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Formal upscaling and numerical validation of unsaturated flow models in fractured porous media
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). University of Bergen, Norway.
Hasselt University, Belgium; University of Sydney, Australia.
Hasselt University, Belgium; University of Bergen, Norway.ORCID iD: 0000-0001-9647-4347
University of Bergen, Norway.
2020 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 407, p. 1-21, article id 109138Article in journal (Refereed) Published
Abstract [en]

In this work, we consider a mathematical model for describing flow in an unsaturated porous medium containing a fracture. Both the flow in the fracture as well as in the matrix blocks are governed by Richards' equation coupled by natural transmission conditions. Using formal asymptotics, we derive upscaled models as the limit of vanishing epsilon, the ratio of the width and length of the fracture. Our results show that the ratio of porosities and permeabilities in the fracture to matrix determine, to the leading order of approximation, the appropriate effective model. In these models the fracture is a lower dimensional object for which different transversally averaged models are derived depending on the ratio of the porosities and permeabilities of the fracture and respective matrix blocks. We obtain a catalogue of effective models which are validated by numerical computations. (C) 2019 Published by Elsevier Inc.

Place, publisher, year, edition, pages
Elsevier, 2020. Vol. 407, p. 1-21, article id 109138
Keywords [en]
Richards' equation, Fractured porous media, Upscaling, Unsaturated flow in porous media
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-77502DOI: 10.1016/j.jcp.2019.109138ISI: 000519535500021OAI: oai:DiVA.org:kau-77502DiVA, id: diva2:1425905
Available from: 2020-04-23 Created: 2020-04-23 Last updated: 2020-06-12Bibliographically approved

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Kumar, Kundan

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • apa.csl
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf