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

Hill, A. A.; Hill, Antony A.; Rajagopal, K. R.; Vergori, L.

Abstract

© 2016, The Author(s). 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.

• Journal Article Type: Article
• Acceptance Date: Apr 4, 2016
• Online Publication Date: Apr 23, 2016
• Publication Date: Jun 1, 2016
• Deposit Date: Jun 6, 2016
• Publicly Available Date: Apr 23, 2017
• Journal: Zeitschrift fur Angewandte Mathematik und Physik
• Print ISSN: 0044-2275
• Electronic ISSN: 1420-9039
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 67
• Issue: 3
• Pages: 49
• DOI: https://doi.org/10.1007/s00033-016-0645-z
• Keywords: Brinkman model, uniqueness, stability of laminar flows
• Public URL: https://uwe-repository.worktribe.com/output/919719
• Publisher URL: http://dx.doi.org/10.1007/s00033-016-0645-z
• Additional Information: Additional Information : The final publication is available at Springer via http://dx.doi.org/http://dx.doi.org/10.1007/s00033-016-0645-z
• Contract Date: Jun 6, 2016