  It is well known that domain-decomposition-based multiscale mixed methods
rely on interface spaces, defined on the skeleton of the decomposition, to
connect the solution among the non-overlapping subdomains. Usual spaces, such
as polynomial-based ones, cannot properly represent high-contrast channelized
features such as fractures (high permeability) and barriers (low permeability)
for flows in heterogeneous porous media. We propose here new interface spaces,
which are based on physics, to deal with permeability fields in the
simultaneous presence of fractures and barriers, accommodated respectively, by
the pressure and flux spaces. Existing multiscale methods based on mixed
formulations can take advantage of the proposed interface spaces, however, in
order to present and test our results, we use the newly developed Multiscale
Robin Coupled Method (MRCM) [Guiraldello, et al., J. Comput. Phys., 355 (2018)
pp. 1-21], which generalizes most well-known multiscale mixed methods, and
allows for the independent choice of the pressure and flux interface spaces. An
adaptive version of the MRCM [Rocha, et al., J. Comput. Phys., 409 (2020),
109316] is considered that automatically selects the physics-based pressure
space for fractured structures and the physics-based flux space for regions
with barriers, resulting in a procedure with unprecedented accuracy. The
features of the proposed approach are investigated through several numerical
simulations of single-phase and two-phase flows, in different heterogeneous
porous media. The adaptive MRCM combined with the interface spaces based on
physics provides promising results for challenging problems with the
simultaneous presence of fractures and barriers.
