GLOBAL WELL-POSEDNESS AND NUMERICAL JUSTIFICATION OF AN EFFECTIVE MICRO-MACRO MODEL FOR REACTIVE TRANSPORT IN ELASTIC PERFORATED MEDIA - Knoch, Jonas; Gahn, Markus; Neuss-Radu, Maria (Multiscale Modeling & Simulation, 2025)
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.
CRIS-Team Scopus Importer:2025-03-14
Keywords: finite element method; global existence and uniqueness; perforated elastic medium; reactive transport; two-scale expansion