论文标题
具有代表性体积元素的非局部多刺。桥接可分离和不可分割的量表
Nonlocal multicontinua with Representative Volume Elements. Bridging separable and non-separable scales
论文作者
论文摘要
最近,用于高对比度和没有规模分离的多尺度模拟的几种方法。其中包括非局部多刺(NLMC)方法,它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,并且可以获得与对比度和尺度无关的最佳收敛结果。但是,这些方法不适合许多多尺度模拟,在许多多尺度模拟中,亚网格效应比粗线分辨率小得多。例如,页岩气的分子动力学与粗晶状尺寸相比,其长度尺度要小得多,即仪表的顺序。在这种情况下,无法探索整个在评估有效特性时的粗网格分辨率。在本文中,我们合并了非本地多孔氏方法的概念和代表性的体积元素(RVE)概念,以探索极端分离的问题。这种方法的第一步是使用子网格量表(sub to rve)编写大型宏观系统。我们称其为中等尺度宏观系统。在下一步中,我们将这个中间宏观系统系统与仿真网格模型相结合,该模型用于模拟。这是使用RVE概念完成的,我们将中间宏观变量与模拟粗网格定义的宏观变量相关联。我们的中间粗制模型允许正确配制宏观变量,并将它们耦合到仿真网格。我们介绍了我们的方法的一般概念,并介绍了单相流的细节。提出了一些数值结果。对于非线性示例,我们使用机器学习技术来计算宏观尺度参数。
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.