Title: Coupling of multiscale and multi-continuum approaches,
Abstract: Simulating complex processes in fractured media requires some type of model
reduction. Well-known approaches include multi-continuum techniques, which have
been commonly used in approximating subgrid effects for flow and transport in
fractured media. Our goal in this paper is to (1) show a relation between
multi-continuum approaches and Generalized Multiscale Finite Element Method
(GMsFEM) and (2) to discuss coupling these approaches for solving problems in
complex multiscale fractured media. The GMsFEM, a systematic approach,
constructs multiscale basis functions via local spectral decomposition in
pre-computed snapshot spaces. We show that GMsFEM can automatically identify
separate fracture networks via local spectral problems. We discuss the relation
between these basis functions and continuums in multi-continuum methods. The
GMsFEM can automatically detect each continuum and represent the interaction
between the continuum and its surrounding (matrix). For problems with
simplified fracture networks, we propose a simplified basis construction with
the GMsFEM. This simplified approach is effective when the fracture networks
are known and have simplified geometries. We show that this approach can
achieve a similar result compared to the results using the GMsFEM with spectral
basis functions. Further, we discuss the coupling between the GMsFEM and
multi-continuum approaches. In this case, many fractures are resolved while for
unresolved fractures, we use a multi-continuum approach with local
Representative Volume Element (RVE) information. As a result, the method deals
with a system of equations on a coarse grid, where each equation represents one
of the continua on the fine grid. We present various basis construction
mechanisms and numerical results.