Global well-posedness and numerical justification of an effective micro-macro model for reactive transport in elastic perforated media

Jonas Knoch; Markus Gahn; Maria Neuss-Radu

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arXiv · 2404.04664

Global well-posedness and numerical justification of an effective micro-macro model for reactive transport in elastic perforated media

Jonas Knoch·Markus Gahn·Maria Neuss-Radu

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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 [25], 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 non-linear 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 {\epsilon} > 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.

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Jonas Knoch, Markus Gahn, Maria Neuss-Radu. 2024-04-06. Global well-posedness and numerical justification of an effective micro-macro model for reactive transport in elastic perforated media. https://arxiv.org/abs/2404.04664

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