2020/07/10 by Bastidas, Manuela, Bringedal, Carina, Pop, Iuliu Sorin
#65M50 #65M55 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA) #[2020] 65M12
paper · doi:10.48550/arxiv.2007.05413
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.