A heterogeneous modeling method for porous media flows

This paper presents a new heterogeneous multiscale modeling method for porous media flows. Physics at the global level is governed by one set of PDEs, while features in the solution that are beyond the resolution capacity of the global model are accounted for by the next refined set of governing equations. In this method, the global or coarse model is given by the Darcy equation, while the local or refined model is given by the Darcy–Stokes equation. Concurrent domain decomposition where global and local models are applied to adjacent subdomains, as well as overlapping domain decomposition where global and local models coexist on overlapping domains, is considered. An interface operator is developed for the case where global and local models commute along the common interface. For the overlapping decomposition, a residual‐based coupling technique is developed that consistently facilitates bottom‐up embedding of scale effects from the local Darcy–Stokes model into the global Darcy model. Numerical results are presented for nonoverlapping and overlapping domain decompositions for various benchmark problems. Computed results show that the hierarchically coupled models accurately account for the heterogeneity of the medium and efficiently incorporate local features into the global response. Copyright © 2014 John Wiley & Sons, Ltd.