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Rigorous upscaling of unsaturated flow in fractured porous media
University of Sydney, Australia; University of Hasselt, Belgium.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
University of Hasselt, Belgium; University of Bergen, Norway.ORCID iD: 0000-0001-9647-4347
University of Bergen, Norway..
2020 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 52, no 1, p. 239-276Article in journal (Refereed) Published
Abstract [en]

In this work, we consider a mathematical model for flow in an unsaturated porous medium containing a fracture. In all subdomains (the fracture and the adjacent matrix blocks) the flow is governed by Richards' equation. The submodels are coupled by physical transmission conditions expressing the continuity of the normal fluxes and of the pressures. We start by analyzing the case of a fracture having a fixed width-length ratio, called epsilon > 0. Then we take the limit epsilon -> 0 and give a rigorous proof for the convergence toward effective models. This is done in different regimes, depending on how the ratio of porosities and permeabilities in the fracture, respectively, in the matrix, scale in terms of epsilon, and leads to a variety of effective models. Numerical simulations confirm the theoretical upscaling results.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2020. Vol. 52, no 1, p. 239-276
Keywords [en]
Richards' equation, fractured porous media, upscaling, unsaturated flow in porous media, existence and uniqueness of weak solutions
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-79221DOI: 10.1137/18M1203754ISI: 000546967700009OAI: oai:DiVA.org:kau-79221DiVA, id: diva2:1456499
Available from: 2020-08-05 Created: 2020-08-05 Last updated: 2020-08-14Bibliographically approved

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Kumar, Kundan

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  • de-DE
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  • nn-NB
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  • Other locale
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Output format
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