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Local existence of strong solutions to micro–macro models for reactive transport in evolving porous media


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Gärttner, Stephan ; Knabner, Peter ; Ray, Nadja:
Local existence of strong solutions to micro–macro models for reactive transport in evolving porous media.
In: European journal of applied mathematics. 35 (2024) 1. - S. 127-154.
ISSN 0956-7925 ; 1469-4425


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Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenised flow and transport equations are solved on the macroscopic scale, while effective parameters are obtained from auxiliary cell problems on possibly evolving reference geometries (micro-scale). Despite their perspective success in rendering lab/field-scale simulations computationally feasible, analytic results regarding the arising two-scale bilaterally coupled system often restrict to simplified models. In this paper, we first derive smooth dependence results concerning the partial coupling from the underlying geometry to macroscopic quantities. Therefore, alterations of the representative fluid domain are described by smooth paths of diffeomorphisms. Exploiting the gained regularity of the effective space- and time-dependent macroscopic coefficients, we present local-in-time existence results for strong solutions to the partially coupled micro–macro system using fixed-point arguments. What is more, we extend our results to the bilaterally coupled diffusive transport model including a level-set description of the evolving geometry.

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Sprache des Eintrags:Englisch
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Mathematisches Institut für Maschinelles Lernen und Data Science (MIDS)
Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Geomatik und Geomathematik
DOI / URN / ID:10.1017/S095679252300013X
Open Access: Freie Zugänglichkeit des Volltexts?:Ja
Verlag:Cambridge University Press
Die Zeitschrift ist nachgewiesen in:
Titel an der KU entstanden:Ja
Eingestellt am: 07. Mai 2024 14:10
Letzte Änderung: 07. Mai 2024 14:10
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