Interface conditions for degenerate two-phase flow equations in one space dimension

Interface conditions for degenerate two-phase flow equations in one space dimension
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一维空间简并两相流方程的界面条件

DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
B. Schweizer
B. Schweizer
中科院分区：
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文献类型：
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作者：
Fulvia Buzzi;Michael Lenzinger;B. Schweizer

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摘要：我们研究了描述多孔材料中油和水运动等的两相流方程，并关注两种不同多孔介质接触的内部界面。在这样的界面处，入口压力关系与系统的简并性一起导致了一种有趣的效应，称为油捕获。限制于一维情况，我们借助适当的正则化和时间离散化来展示存在结果。关键的工具是紧致引理：测度空间中时间导数的控制用于得出序列的强收敛性。
Abstract We study the two-phase flow equations describing, e.g., the motion of oil and water in a porous material, and are concerned with interior interfaces where two different porous media are in contact. At such an interface, the entry pressure relation together with the degeneracy of the system leads to an interesting effect known as oil-trapping. Restricting to the one-dimensional case we show an existence result with the help of appropriate regularizations and a time discretization. The crucial tool is a compactness lemma: The control of the time derivative in a space of measures is used to conclude the strong convergence of a sequence.