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Recently, several approaches for multiscale simulations for problems withhigh contrast and no scale separation are introduced. Among them is thenonlocal multicontinua (NLMC) method, which introduces multiple macroscopicvariables in each computational grid. These approaches explore the entirecoarse block resolution and one can obtain optimal convergence resultsindependent of contrast and scales. However, these approaches are not amenableto many multiscale simulations, where the subgrid effects are much smaller thanthe coarse-mesh resolution. For example, the molecular dynamics of shale gasoccurs in much smaller length scales compared to the coarse-mesh size, which isof orders of meters. In this case, one can not explore the entire coarse-gridresolution in evaluating effective properties. In this paper, we merge theconcepts of nonlocal multicontinua methods and Representative Volume Element(RVE) concepts to explore problems with extreme scale separation. The firststep of this approach is to use sub-grid scale (sub to RVE) to write alarge-scale macroscopic system. We call it intermediate scale macroscalesystem. In the next step, we couple this intermediate macroscale system to thesimulation grid model, which are used in simulations. This is done using RVEconcepts, where we relate intermediate macroscale variables to the macroscalevariables defined on our simulation coarse grid. Our intermediate coarse modelallows formulating macroscale variables correctly and coupling them to thesimulation grid. We present the general concept of our approach and presentdetails of single-phase flow. Some numerical results are presented. Fornonlinear examples, we use machine learning techniques to compute macroscaleparameters.

Nonlocal multicontinua with Representative Volume Elements. Bridging separable and non-separable scales