One-phase Newtonian flow
One-phase Newtonian flow
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单相牛顿流
DOI：
10.1007/978-1-4612-1920-0_3
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
G. Allaire
中科院分区：
文献类型：
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作者：
G. Allaire
本节致力于推导在多孔介质中流动的不可压缩粘性流体的达西定律。从周期多孔介质中定常的Stokes方程出发，在固体孔隙上采用无滑移(Dirichlet)边界条件，利用双尺度收敛方法，通过周期均匀化，严格地得到了达西定律。假设多孔介质的周期性是不现实的，但它允许将这个问题放在一个非常简单的框架中，并不需要太多的努力就能证明定理。我们用e表示周期与多孔介质总尺寸的比率。这是我们渐近分析的小参数，因为孔隙大小通常比储集层的特征长度小得多。多孔介质包含在区域Q中，其流体部分用TE表示。从数学的角度来看，513E是一个周期性穿孔的区域，即它有许多大小为e的小孔，这些小孔代表流体无法穿透的固体障碍物。
This section is devoted to the derivation of Darcy’s law for an incompressible viscous fluid flowing in a porous medium. Starting from the steady Stokes equations in a periodic porous medium, with a no-slip (Dirichlet) boundary condition on the solid pores, Darcy’s law is rigorously obtained by periodic homogenization using the two-scale convergence method. The assumption of the periodicity of the porous medium is by no means realistic, but it allows casting this problem in a very simple framework and proving theorems without too much effort. We denote by e the ratio of the period to the overall size of the porous medium. It is the small parameter of our asymptotic analysis because the pore size is usually much smaller than the characteristic length of the reservoir. The porous medium is contained in a domain Q, and its fluid part is denoted by TE. From a mathematical point of view, 513E is a periodically perforated domain, i.e., it has many small holes of size e which represent solid obstacles that the fluid cannot penetrate.