  Recently, several approaches for multiscale simulations for problems with
high contrast and no scale separation are introduced. Among them is the
nonlocal multicontinua (NLMC) method, which introduces multiple macroscopic
variables in each computational grid. These approaches explore the entire
coarse block resolution and one can obtain optimal convergence results
independent of contrast and scales. However, these approaches are not amenable
to many multiscale simulations, where the subgrid effects are much smaller than
the coarse-mesh resolution. For example, the molecular dynamics of shale gas
occurs in much smaller length scales compared to the coarse-mesh size, which is
of orders of meters. In this case, one can not explore the entire coarse-grid
resolution in evaluating effective properties. In this paper, we merge the
concepts of nonlocal multicontinua methods and Representative Volume Element
(RVE) concepts to explore problems with extreme scale separation. The first
step of this approach is to use sub-grid scale (sub to RVE) to write a
large-scale macroscopic system. We call it intermediate scale macroscale
system. In the next step, we couple this intermediate macroscale system to the
simulation grid model, which are used in simulations. This is done using RVE
concepts, where we relate intermediate macroscale variables to the macroscale
variables defined on our simulation coarse grid. Our intermediate coarse model
allows formulating macroscale variables correctly and coupling them to the
simulation grid. We present the general concept of our approach and present
details of single-phase flow. Some numerical results are presented. For
nonlinear examples, we use machine learning techniques to compute macroscale
parameters.
