非局部多连续体升维法用于破碎多孔介质中的多连续体流动问题
Nonlocal multicontinua upscaling for multicontinua flow problems in fractured porous media
AI总结：
本文提出一种非局部多连续体升维方法，用于破碎多孔介质中的多连续体流动问题，通过多尺度基函数有效捕捉矩阵连续体与离散裂缝的相互作用。
摘要：
本文旨在开发一种新的多连续体流动问题的非局部多连续体（NLMC）升维方法。我们考虑一个描述多孔介质中多重流动变量的方程组，这些变量定义在基质和裂缝上。为了构建我们的升维模型，我们将应用非局部多连续体升维技术。升维系数通过使用多尺度基函数获得，这些基函数是定义在超采样区域上的局部问题的解。对于每个目标粗网格元素内的连续体，我们将解一个通过扩展目标元素几层粗网格得到的超采样区域上的局部问题，并设置约束条件，使局部解在选定的连续体上具有均值为一，其他部分为零均值。所得到的多尺度基函数已显示出良好的近似性质。为了说明我们的方法思路，我们将考虑一个由两个空间维度中离散裂缝组成的双连续体背景模型，即我们考虑一个具有三个连续体的系统。我们将展示几个数值例子，这些例子表明我们的方法能够有效地在粗网格上捕捉基质连续体和离散裂缝之间的相互作用。
英文摘要：
Our goal of this paper is to develop a new upscaling method for multicontinua flow problems in fractured porous media. We consider a system of equations that describes flow phenomena with multiple flow variables defined on both matrix and fractures. To construct our upscaled model, we will apply the nonlocal multicontinua (NLMC) upscaling technique. The upscaled coefficients are obtained by using some multiscale basis functions, which are solutions of local problems defined on oversampled regions. For each continuum within a target coarse element, we will solve a local problem defined on an oversampling region obtained by extending the target element by few coarse grid layers, with a set of constraints which enforce the local solution to have mean value one on the chosen continuum and zero mean otherwise. The resulting multiscale basis functions have been shown to have good approximation properties. To illustrate the idea of our approach, we will consider a dual continua background model consisting of discrete fractures in two space dimensions, that is, we consider a system with three continua. We will present several numerical examples, and they show that our method is able to capture the interaction between matrix continua and discrete fractures on the coarse grid efficiently.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
