  In this paper, we combine concepts of the generalized multiscale finite
element method and mode decomposition methods to construct a robust
local-global approach for model reduction of flows in high-contrast porous
media. This is achieved by implementing proper orthogonal decomposition (POD)
and dynamic mode decomposition (DMD) techniques on a coarse grid. The resulting
reduced-order approach enables a significant reduction in the flow problem size
while accurately capturing the behavior of fully resolved solutions. We
consider a variety of high-contrast coefficients and present the corresponding
numerical results to illustrate the effectiveness of the proposed technique.
This paper is a continuation of the first part where we examine the
applicability of POD and DMD to derive simplified and reliable representations
of flows in high-contrast porous media. In the current paper, we discuss how
these global model reduction approaches can be combined with local techniques
to speed-up the simulations. The speed-up is due to inexpensive, while
sufficiently accurate, computations of global snapshots.
