Homogenization of the degenerate two-phase flow equations
Homogenization of the degenerate two-phase flow equations
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DOI：
10.1142/s0218202513500334
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发表时间：
2013-08
影响因子：
3.5
通讯作者：
P. Henning;Mario Ohlberger;B. Schweizer
中科院分区：
文献类型：
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作者：
P. Henning;Mario Ohlberger;B. Schweizer
我们分析了高度非均质介质中的两相流。用加权解的新概念处理渗透系数函数的退化问题。我们用渗透率与压力乘积的加权压力函数ψ代替压力变量来表述问题。我们进行了均匀化极限，得到了双尺度极限系统形式的有效方程。在非简并情况下，非线性有效系统具有经典形式。在简并情况下，双尺度系统再次使用加权压力变量。我们的方法可以在没有全局压力函数的情况下工作。即使包括内部界面，我们的方法也提供了均匀化极限，而不需要对渗透率或毛细压力进行任何小假设。
We analyze two-phase flow in highly heterogeneous media. Problems related to the degeneracy of the permeability coefficient functions are treated with a new concept of weighted solutions. Instead of the pressure variables we formulate the problem with the weighted pressure function ψ, which is obtained as the product of permeability and pressure. We perform the homogenization limit and obtain effective equations in the form of a two-scale limit system. The nonlinear effective system is of the classical form in the non-degenerate case. In the degenerate case, the two-scale system uses again a weighted pressure variable. Our approach allows to work without the global pressure function. Even though internal interfaces are included, our approach provides the homogenization limit without any smallness assumptions on permeabilities or capillary pressures.