1. Global well-posedness and numerical justification of an effective micro-macro model for reactive transport in elastic perforated media
- Author
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Knoch, Jonas, Gahn, Markus, and Neuss-Radu, Maria
- Subjects
Mathematics - Analysis of PDEs ,35A01, 35B27, 35M30, 35K57, 65M60, 74Q05 - 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.
- Published
- 2024