Averaging of flows with capillary hysteresis in stochastic porous media
Averaging of flows with capillary hysteresis in stochastic porous media
复制标题
随机多孔介质中毛细管滞后的流量平均
DOI：
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发表时间：
2007
影响因子：
1.9
通讯作者：
B. Schweizer
中科院分区：
文献类型：
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作者：
B. Schweizer
不饱和多孔介质中的流体通过压力 (p) 和饱和度 (u) 之间的关系来描述。达西定律和质量守恒定律提供了 u 的演化方程，毛细管压力提供了 p 和 u 之间的关系，其形式为 p∈ pc(u,∂tu)。多值函数pc会导致滞后效应。我们构建了滞后系统的弱解和强解，并对系统的振荡随机系数进行均质化。有效方程包含一个新的因变量，该变量对润湿过程的历史进行编码，并提供对物理系统的更好描述。
Fluids in unsaturated porous media are described by the relationship between pressure (p) and saturation (u). Darcy's law and conservation of mass provides an evolution equation for u, and the capillary pressure provides a relation between p and u of the form p∈ pc(u,∂tu). The multi-valued function pc leads to hysteresis effects. We construct weak and strong solutions to the hysteresis system and homogenize the system for oscillatory stochastic coefficients. The effective equations contain a new dependent variable that encodes the history of the wetting process and provide a better description of the physical system.