GLOBAL WELL-POSEDNESS AND NUMERICAL JUSTIFICATION OF AN EFFECTIVE MICRO-MACRO MODEL FOR REACTIVE TRANSPORT IN ELASTIC PERFORATED MEDIA

Knoch J, Gahn M, Neuss-Radu M (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Multiscale Modeling & Simulation Society for Industrial and Applied Mathematics

Book Volume: 23

Pages Range: 458-485

Journal Issue: 1

DOI: 10.1137/24M1644304

Abstract

In this paper, we investigate an effective model for reactive transport in elastically deformable perforated media. This model was derived by formal asymptotic expansions in [J. Knoch, M. Gahn, M. Neuss-Radu, and N. Neuβ, Transp. Porous Media, 147 (2023), pp. 93-123], starting from a microscopic model consisting of a linear elasticity problem on a fixed domain, i.e., in the Lagrangian framework, and a problem for reactive transport on the current deformed domain, i.e., in the Eulerian framework. The effective model is of micro-macro type and features strong nonlinear couplings. Here, we prove global existence in time and uniqueness for the effective micro-macro model under a smallness assumption for the data of the macroscopic elasticity subproblem. Moreover, we show numerically the convergence of microscopic solutions towards the solution of the effective model when the scale parameter ε > 0 becomes smaller and smaller, and also compute the approximation error. The numerical justification of the formally derived effective micro-macro model is particularly important, as rigorous analytical convergence proofs or error estimates are not available so far. Finally, we compare the effective micro-macro model with alternative, simpler effective descriptions of transport in elastic perforated media.

Authors with CRIS profile

Jonas Knoch Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen) Maria Neuß Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Ruprecht-Karls-Universität Heidelberg DE Germany (DE)

How to cite

APA:

Knoch, J., Gahn, M., & Neuss-Radu, M. (2025). GLOBAL WELL-POSEDNESS AND NUMERICAL JUSTIFICATION OF AN EFFECTIVE MICRO-MACRO MODEL FOR REACTIVE TRANSPORT IN ELASTIC PERFORATED MEDIA. Multiscale Modeling & Simulation, 23(1), 458-485. https://doi.org/10.1137/24M1644304

MLA:

Knoch, Jonas, Markus Gahn, and Maria Neuss-Radu. "GLOBAL WELL-POSEDNESS AND NUMERICAL JUSTIFICATION OF AN EFFECTIVE MICRO-MACRO MODEL FOR REACTIVE TRANSPORT IN ELASTIC PERFORATED MEDIA." Multiscale Modeling & Simulation 23.1 (2025): 458-485.

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