On the stability and uniqueness of the flow of a fluid through a porous medium

Hill, A. A., Rajagopal, K. R. and Vergori, L. (2016) On the stability and uniqueness of the flow of a fluid through a porous medium. Zeitschrift für Angewandte Mathematik und Physik, 67, 49. (doi: 10.1007/s00033-016-0645-z)

Abstract

In this short note we study the stability of flows of a fluid through porous media that satisfies a generalization of Brinkman’s equation to include inertial effects. Such flows could have relevance to enhanced oil recovery and also to the flow of dense liquids through porous media. In any event, one cannot ignore the fact that flows through porous media are inherently unsteady and thus at least a part of the inertial term needs to be retained in many situations. We study the stability of the rest state and find it to be asymptotically stable. Next, we study the stability of a base flow and find that the flow is asymptotically stable, provided the base flow is sufficiently slow. Finally, we establish results concerning the uniqueness of the flow under appropriate conditions, and present some corresponding numerical results.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Vergori, Dr Luigi
• Authors: Hill, A. A., Rajagopal, K. R., and Vergori, L.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Zeitschrift für Angewandte Mathematik und Physik
• Publisher: Springer-Verlag
• ISSN: 0044-2275
• ISSN (Online): 1420-9039
• Published Online: 23 April 2016
• Copyright Holders: Copyright © 2016 The Authors
• First Published: First published in Zeitschrift für Angewandte Mathematik und Physik 67:49
• Publisher Policy: Reproduced under a Creative Commons License