  In this paper we propose a method for the construction of locally
conservative flux fields from Generalized Multiscale Finite Element Method
(GMsFEM) pressure solutions. The flux values are obtained from an element-based
postprocessing procedure in which an independent set of 4x4 linear systems need
to be solved. To test the performance of the method we consider two
heterogeneous permeability coefficients and couple the resulting fluxes to a
two-phase flow model. The increase in accuracy associated with the computation
of the GMsFEM pressure solutions is inherited by the postprocessed flux fields
and saturation solutions, and is closely correlated to the size of the
reduced-order systems. In particular, the addition of more basis functions to
the enriched coarse space yields solutions that more accurately capture the
behavior of the fine scale model. A number of numerical examples are offered to
validate the performance of the method.
