Instability of gravity wetting fronts for Richards equations with hysteresis
Instability of gravity wetting fronts for Richards equations with hysteresis
复制标题
具有滞后现象的理查兹方程的重力润湿前沿的不稳定性
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
B. Schweizer
中科院分区：
文献类型：
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作者：
B. Schweizer
研究了多孔介质中饱和度剖面的演化规律。当在较不饱和的介质之上有较饱和的介质时，重力的作用是液体的向下运动。虽然在实验中可以观察到指进效应，即平面前沿解的不稳定性，但在不同的设置中已经验证了具有重力的理查兹方程具有稳定的平面前沿。在目前的工作中，我们分析了理查兹方程耦合到一个播放型滞后模型中的毛管压力关系。我们的结果是，在适当的几何形状和适当的初始和边界条件，平面前的解决方案是不稳定的。特别是，我们发现，理查兹方程的重力和滞后不定义一个L-收缩。
We study the evolution of saturation profiles in a porous medium. When there is a more saturated medium on top of a less saturated medium, the effect of gravity is a downward motion of the liquid. While in experiments the effect of fingering can be observed, i.e. an instability of the planar front solution, it has been verified in different settings that the Richards equation with gravity has stable planar fronts. In the present work we analyze the Richards equation coupled to a play-type hysteresis model in the capillary pressure relation. Our result is that, in an appropriate geometry and with adequate initial and boundary conditions, the planar front solution is unstable. In particular, we find that the Richards equation with gravity and hysteresis does not define an L-contraction.