Homogenization theory and nonlinearities in Darcy's law

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-04 DOI:10.28927/sr.2024.012622

K. Guerra, C. Romanel

引用次数: 0

Abstract

The theory of homogenization of differential equations has become an open field of research in several areas of the exact sciences and has proved to be a powerful tool for understanding the global behavior of heterogeneous materials. Despite knowing that the deduction of Darcy’s law through the Navier-Stokes equations has been debated for decades, many questions remain open, mainly regarding more complex boundary conditions, cases involving multiphase flows and the numerical homogenization techniques. It is known today that Darcy’s law is presented in the form of a linear relationship only for a range of hydraulic gradient and that this range overlaps the range of laminar flow through soil voids. Therefore, it is proposed in this work to understand the loss of linearity in Darcy’s law, based on the theory of homogenization, modifying and exploring the limit results obtained by Allaire in 1991.

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达西定律中的均质化理论和非线性问题

微分方程均质化理论已成为精密科学多个领域的一个开放式研究领域，并被证明是理解异质材料全局行为的有力工具。尽管通过纳维-斯托克斯方程对达西定律的推导已经争论了几十年，但许多问题仍然悬而未决，主要涉及更复杂的边界条件、涉及多相流的情况以及数值均质化技术。目前已知，达西定律仅在一定的水力梯度范围内以线性关系的形式呈现，而这一范围与通过土壤空隙的层流范围重叠。因此，本研究建议以均质化理论为基础，修改和探索 Allaire 于 1991 年获得的极限结果，以理解达西定律中线性关系的丧失。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.