Modeling of multiphase flow and transport in highly heterogeneous porous media must capture a broad range of coupled spatial and temporal scales. Recently, a hierarchical approach dubbed the Multilevel Multiscale Mimetic (M³) method, was developed to simulate two-phase flow in porous media. The M³ method is locally mass conserving at all levels in its hierarchy, it supports unstructured polygonal grids and full tensor permeabilities, and it can achieve large coarsening factors. In this work we consider infiltration of water into a two-dimensional layered medium. The grid is aligned with the layers but not the coordinate axes. We demonstrate that with an efficient temporal updating strategy for the coarsening parameters, fine-scale accuracy of prominent features in the flow is maintained by the M³ method.