Recently, several approaches for multiscale simulations for 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 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, 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 cannot 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.

最近，针对高对比度和无标度分离的问题，提出了几种用于多标度模拟的方法。其中包括非局部多连续体（NLMC）方法，该方法在每个计算网格中引入了多个宏观变量。这些方法探索了整个粗块分辨率，并且可以获得独立于对比度和比例的最佳收敛结果。但是，这些方法不适用于许多多尺度模拟，在这些模拟中，子网格效果远小于粗网格分辨率。例如，与几米级的粗筛网尺寸相比，页岩气的分子动力学发生的长度尺度要小得多。在这种情况下，无法在评估有效属性时探索整个粗网格分辨率。在本文中，我们将非局部多连续体方法的概念与代表性体积元素（RVE）概念进行了合并，以探索极端尺度分离的问题。这种方法的第一步是使用子网格规模（隶属于RVE）来编写大型宏观系统。我们称其为中等规模的宏观系统。在下一步中，我们将此中间宏系统耦合到仿真网格模型，该模型用于仿真。这是使用RVE概念完成的，其中我们将中间宏尺度变量与在模拟粗网格上定义的宏尺度变量相关联。我们的中间粗模型允许正确地制定宏变量并将其耦合到模拟网格。我们介绍了该方法的一般概念，并介绍了单相流的详细信息。给出了一些数值结果。