Homogenization of the inviscid incompressible fluid flow through a 2D porous medium
Homogenization of the inviscid incompressible fluid flow through a 2D porous medium
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DOI：
10.1090/s0002-9939-99-05062-5
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发表时间：
1999-02
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影响因子：
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通讯作者：
A. Mikelić;L. Paoli
中科院分区：
文献类型：
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作者：
A. Mikelić;L. Paoli
考虑二维多孔介质中的非定常不可压缩欧拉方程。我们假设一种周期多孔介质，其周期与特征孔径e成正比，流体部分连通。流动受到外力的作用，对应于流入。从初始无旋速度出发，证明了有效过滤速度满足暂态过滤规律。它与达西定律有相似之处，但它现在将过滤速度的时间导数与压力梯度联系起来。黏度不再出现在过滤律中，渗透率张量由分解型辅助问题确定。利用极限问题，我们构造了流体速度的修正，并证明了C1([0, T]; L2（Ω）2)-误差的范数为e阶。同样，我们估计流体压力与其在C（[0, T]; L1（Ω））中的修正之间的差为Ce。
We consider the non-stationary incompressible Euler equations in a 2D porous medium. We suppose a periodic porous medium, with the period proportional to the characteristic pore size e and with connected fluid part. The flow is subject to an external force, corresponding to an inflow. We start from an initial irrotational velocity and prove that the effective filtration velocity satisfies a transient filtration law. It has similarities with Darcy’s law, but it now connects the time derivative of the filtration velocity with the pressure gradient. The viscosity does not appear in the filtration law any more and the permeability tensor is determined through auxiliary problems of decomposition type. Using the limit problem, we construct the correction for the fluid velocity and prove that C1([0, T ]; L2(Ω)2)-norm of the error is of order e. Similarly, we estimate the difference between the fluid pressure and its correction in C([0, T ]; L1(Ω)) as Ce.