NDLI: Asymptotics for the Muskat problem

Content Provider	Springer Nature Link
Author	Booth, R. J. S.
Copyright Year	2010
Abstract	The Muskat problem is a simple model for the displacement of one fluid by another in a porous medium or Hele-Shaw cell. Solutions of the problem are unstable to small-wavelength disturbances, and there is evidence that the problem is ill-posed. A well-posed problem may be developed by including additional regularising physical effects, primarily surface tension. In practical situations involving oil recovery, one can engineer for there to be a gradual change in the viscosity of the fluids, either by the gradual introduction of a polymer capable of altering the viscosity of water, or by gradual diffusion between two miscible fluids. The regularising effect of smoothing the initial data is investigated. Thus rather than a sharp interface between the two fluids, and therefore a sharp jump in viscosity, there is a smooth transition from one viscosity to another. It is shown how the standard Muskat problem may be recovered as an asymptotic limit and the effective free-surface model that may be recovered is discussed. The stability of solutions to the smoothed Muskat problem is investigated, and the important effect of smoothing for disturbances with a large wavenumber is demonstrated.
Starting Page	155
Ending Page	168
Page Count	14
File Format	PDF
ISSN	00220833
Journal	Journal of Engineering Mathematics
Volume Number	69
Issue Number	2-3
e-ISSN	15732703
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-04-29
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Asymptotic analysis Free-boundary problem Muskat problem Polymer flooding Smoothing Numeric Computing Mathematical Modeling and Industrial Mathematics Analysis Applications of Mathematics Mechanics
Content Type	Text
Resource Type	Article
Subject	Mathematics Engineering

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