A POD-EIM reduced two-scale model for precipitation in porous media

A time-dependent two-scale multiphase model for precipitation in porous media is considered, which has recently been proposed and investigated numerically. For numerical treatment, the microscale model needs to be finely resolved due to moving discontinuities modelled by several phase-field functions. This results in high computational demands due to the need of resolving many such highly resolved cell problems in course of the two-scale simulation. In this article, we present a model order reduction technique for this model, which combines different ingredients such as proper orthogonal decomposition for construction of the approximating spaces, the empirical interpolation method for parameter dependency and multiple basis sets for treating the high solution variability. The resulting reduced model experimentally demonstrates considerable acceleration and good accuracy both in reproduction as well as generalization experiments.