A Multilevel Multiscale Mimetic (M3) Method for an Anisotropic Infiltration Problem

Modeling of multiphase flow and transport in highly hetero­ geneous 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 flows in porous media. The M3 method is locally mass conserving at all levels in its hierarchy, it supports unstructured polyhedral grids and full tensor permeabilities, and it can achieve large coarsening factors . In this work we consider infiltration of water into a two-dimensional lay­ ered 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. Even for large coarsening factors, with which we achieve a speedup of xx times.