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

Gärttner S, Knabner P, Ray N (2024)


Publication Type: Journal article

Publication year: 2024

Journal

Book Volume: 35

Pages Range: 127-154

Journal Issue: 1

DOI: 10.1017/S095679252300013X

Abstract

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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How to cite

APA:

Gärttner, S., Knabner, P., & Ray, N. (2024). Local existence of strong solutions to micro-macro models for reactive transport in evolving porous media. European Journal of Applied Mathematics, 35(1), 127-154. https://doi.org/10.1017/S095679252300013X

MLA:

Gärttner, Stephan, Peter Knabner, and Nadja Ray. "Local existence of strong solutions to micro-macro models for reactive transport in evolving porous media." European Journal of Applied Mathematics 35.1 (2024): 127-154.

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