An adaptive multi-scale iterative scheme for a phase-field model for precipitation and dissolution in porous media

Abstract

Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in time in an apriori unknown manner. To deal with such aspects, we here adopt a two-scale phase-field model, and propose a robust scheme for the numerical approximation of the solution. The scheme takes into account both the scale separation in the model, as well as the non-linear character of the model. After proving the convergence of the scheme, an adaptive two-scale strategy is incorporated, which improves the efficiency of the simulations. Numerical tests are presented, showing the efficiency and accuracy of the scheme in the presence of anisotropies and heterogeneities.

Multi-Scale Modeling and Simulation of Transport Processes in an Elastically Deformable Perforated Medium

“…Additionally, adaptive schemes such as clustering "similar" cell problems and solving only one representative cell problem per cluster are conceivable and have been successfully applied in the context of multi-scale models, see e.g. Bastidas et al (2020); Gärttner et al (2020).…”