Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?
Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?
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DOI：
10.1016/j.advwatres.2013.09.006
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发表时间：
2013-12-01
影响因子：
4.7
通讯作者：
Quintard, Michel
中科院分区：
文献类型：
--
作者：
Davit, Yohan;Bell, Christopher G.;Quintard, Michel
各种各样的技术已经发展到均匀化的输运方程在多尺度和多相系统。这产生了一个丰富多样的领域，但也导致了孤立的科学社区和脱节的文学机构的出现。在这里，我们的目标是弥合正式的多尺度渐近和体积平均理论之间的差距。我们通过一个简单的示例应用程序描述了一个抛物线运输问题的方法，并在这样做，比较各自的优点/缺点，从实际的角度来看。本文还旨在作为教学指南，并可被视为研究生的教程，因为我们提供了历史背景，非常小心地详细说明了微妙的点，并参考了许多基本的作品。(C)2013爱思唯尔有限公司保留所有权利。
A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works. (C) 2013 Elsevier Ltd. All rights reserved.