论文标题
在多孔介质中流动，孔的断裂
Flow in Porous Media with Fractures of Varying Aperture
论文作者
论文摘要
我们以宏观尺度研究骨折的多孔培养基中的单相流，该流量可以单独建模裂缝。该流程受裂缝和多孔矩阵的达西定律管辖。我们得出了一种新的混合维度模型，其中裂缝由$（n-1）$ - 尺寸接口表示$ n $二维子域，$ n \ ge 2 $。特别是，我们通过考虑具有空间变化的不对称裂缝来考虑[22]中模型的概括。因此，新模型对于描述表面粗糙度或建模曲线或绕组裂缝特别方便。在适当的条件下证明了新模型的良好性。此外，我们制定了新模型不连续的盖尔金离散化，并通过执行二维数值实验来验证模型。
We study single-phase flow in a fractured porous medium at a macroscopic scale that allows to model fractures individually. The flow is governed by Darcy's law in both fractures and porous matrix. We derive a new mixed-dimensional model, where fractures are represented by $(n-1)$-dimensional interfaces between $n$-dimensional subdomains for $n\ge 2$. In particular, we suggest a generalization of the model in [22] by accounting for asymmetric fractures with spatially varying aperture. Thus, the new model is particularly convenient for the description of surface roughness or for modeling curvilinear or winding fractures. The wellposedness of the new model is proven under appropriate conditions. Further, we formulate a discontinuous Galerkin discretization of the new model and validate the model by performing two- and three-dimensional numerical experiments.
