Sharp convergence rates for Darcy’s law
Sharp convergence rates for Darcy’s law
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DOI：
10.1080/03605302.2022.2037634
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发表时间：
2020-11
影响因子：
1.9
通讯作者：
Zhongwei Shen
中科院分区：
文献类型：
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作者：
Zhongwei Shen
本文讨论了不可压缩粘性流体在多孔介质中流动的达西定律。我们在周期穿孔有界域上证明了其收敛速度，其中ε表示固体障碍的大小。这是通过构造两个边界层校正器来实现的，以控制不可压缩条件以及解与其渐近展开中的主导项之间的边值差所产生的边界层。其中一个校正器处理切向边界数据，而另一个校正器处理法向边界数据。
Abstract This article is concerned with Darcy’s law for an incompressible viscous fluid flowing in a porous medium. We establish the sharp convergence rate in a periodically perforated and bounded domain in for where ε represents the size of solid obstacles. This is achieved by constructing two boundary layer correctors to control the boundary layers created by the incompressibility condition and the discrepancy of boundary values between the solution and the leading term in its asymptotic expansion. One of the correctors deals with the tangential boundary data, while the other handles the normal boundary data.