论文标题
Darcy定律的理论推导了稀疏介质中流体流动
Theoretical derivation of Darcy's law for fluid flow in thin porous media
论文作者
论文摘要
在本文中，我们研究了稀薄的多孔介质中固定的不可压缩牛顿流体流动。正在考虑的媒体是一个限制的$ 3D $域，限制在两个平行板之间。该域的描述包括两个小参数：$ \ varepsilon $代表Pates和$ a_ \ varepsilon $连接到域的微结构，以至于$ a_ \ varepsilon \ ll \ ll \ varepsilon $。我们考虑穿孔介质的经典设置，即$ a_ \ varepsilon $ - 周期分布的固体（未连接）尺寸$ a_ \ varepsilon $。本文的目的是引入一个版本的展开方法，具体取决于参数$ \ varepsilon $和$ a_ \ varepsilon $，然后得出相应的$ 2D $ darcy的定律。
In this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is a bounded perforated $3D$ domain confined between two parallel plates. The description of the domain includes two small parameters: $\varepsilon$ representing the distance between pates and $a_\varepsilon$ connected to the microstructure of the domain such that $a_\varepsilon\ll \varepsilon$. We consider the classical setting of perforated media, i.e. $a_\varepsilon$-periodically distributed solid (not connected) obstacles of size $a_\varepsilon$. The goal of this paper is to introduce a version of the unfolding method, depending on both parameters $\varepsilon$ and $a_\varepsilon$, and then to derive the corresponding $2D$ Darcy's law.
