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Rigorous upscaling of rough boundaries for reactive flows
Center for Subsurface Modeling, The Uni versity of Texas at Austin, USA.
Supply Chain Development, Jumbo Supermarkten B.V., The Netherlands.
Department of Mathematics and Computer Sciences, Eindhoven University of Technology, The Netherlands & Institute of Mathematics, University of Bergen, Bergen, Norway.
2014 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 94, no 7-8, p. 623-644Article in journal (Refereed) Published
Abstract [en]

We consider a mathematical model for reactive flow in a channel having a rough (periodically oscillating) boundary with both period and amplitude ε. The ions are being transported by the convection and diffusion processes. These ions can react at the rough boundaries and get attached to form the crystal (precipitation) and become immobile. The reverse process of dissolution is also possible. The model involves non‐linear and multi‐valued rates and is posed in a fixed geometry with rough boundaries. We provide a rigorous justification for the upscaling process in which we define an upscaled problem defined in a simpler domain with flat boundaries. To this aim, we use periodic unfolding techniques combined with translation estimates. Numerical experiments confirm the theoretical predictions and illustrate a practical application of this upscaling process.

Place, publisher, year, edition, pages
John Wiley & Sons, 2014. Vol. 94, no 7-8, p. 623-644
Keywords [en]
Reactive flows, rough boundaries, homogenization
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-69511DOI: 10.1002/zamm.201200226ISI: 000339009400005OAI: oai:DiVA.org:kau-69511DiVA, id: diva2:1253837
Available from: 2018-10-06 Created: 2018-10-06 Last updated: 2018-10-16Bibliographically approved

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Kumar, Kundan

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