Nonlocal multicontinua with representative volume elements. Bridging separable and non-separable scales

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