  We consider the coupled system of equations that describe flow in fractured
porous media. To describe such types of problems, multicontinuum and multiscale
approaches are used. Because in multicontinuum models, the permeability of each
continuum has a significant difference, a large number of iterations is
required for the solution of the resulting linear system of equations at each
time iteration. The presented decoupling technique separates equations for each
continuum that can be solved separately, leading to a more efficient
computational algorithm with smaller systems and faster solutions. This
approach is based on the additive representation of the operator with
semi-implicit approximation by time, where the continuum coupling part is taken
from the previous time layer. We apply, analyze and numerically investigate
decoupled schemes for classical multicontinuum problems in fractured porous
media on sufficiently fine grids with finite volume approximation. We show that
the decoupled schemes are stable, accurate, and computationally efficient.
Next, we extend and investigate this approach for multiscale approximation on
the coarse grid using the nonlocal multicontinuum (NLMC) method. In NLMC
approximation, we construct similar decoupled schemes with the same continuum
separation approach. A numerical investigation is presented for model problems
with two and three-continuum in the two-dimensional formulation.
