Distributed Microstructure Models of Porous Media
Distributed Microstructure Models of Porous Media
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多孔介质的分布式微观结构模型
DOI：
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发表时间：
1993
期刊：
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通讯作者：
R. Showalter
中科院分区：
文献类型：
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作者：
R. Showalter
通过裂隙或其他高度不均匀介质的层流会导致具有快速振荡系数的方程的非常奇异的初始边界值问题。极限情况（通过均质化）是模型单元的连续分布，它代表有限（奇异）情况的有效近似，我们调查了此类系统理论的一些最新结果。这是作为巴拿赫空间连续直和的应用而开发的，巴拿赫空间作为相应（静态）变分或（时间）动态问题的能量或状态空间而自然出现。我们讨论完全裂隙介质的基本模型、部分裂隙介质中二次通量的扩展，以及作为微观结构模型的极限情况实现的经典模型系统。
Laminar flow through fissured or otherwise highly inhomogeneous media leads to very singular initial-boundary-value problems for equations with rapidly oscillating coefficients. The limiting case (by homogenization) is a continuous distribution of model cells which represent a valid approximation of the finite (singular) case, and we survey some recent results on the theory of such systems. This is developed as an application of continuous direct sums of Banach spaces which arise rather naturally as the energy or state spaces for the corresponding (stationary) variational or (temporal) dynamic problems. We discuss the basic models for a totally fissured medium, the extension to include secondary flux in partially fissured media, and the classical model systems which are realized as limiting cases of the microstructure models.