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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Continuum Models of Two-Phase Flow in Porous Media
- Shearer\, M (North Carolina State University)
DTSTART;TZID=Europe/London:20130611T120000
DTEND;TZID=Europe/London:20130611T130000
UID:TALK45725AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/45725
DESCRIPTION:I discuss two models of two-phase fluid flow in wh
ich undercompressive shock waves have been discove
red recently. In the first part of the talk\, the
focus is on two-phase flow in porous media. Plane
waves are modeled by the one-dimensional Buckley-
Leverett equation\, a scalar conservation law. T
he Gray-Hassanizadeh model for rate-dependent capi
llary pressure adds dissipation and a BBM-type d
ispersion\, giving rise to undercompressive waves.
Two-phase flow in porous media is notoriously su
bject to fingering instabilities\, related to the
classic Saffman-Taylor instability. However\, a
two dimensional linear stability analysis of shar
p planar interfaces reveals a criterion predictin
g that weak Lax shocks may be stable or unstable t
o long-wave two-dimensional perturbations. This su
rprising result is related to the hyperbolic-ellip
tic nature of the system of linearized equations.
Numerical simulations of the full nonlinear sys
tem of equations\, including dissipation and dispe
rsion\, verify the stability predictions at the h
yperbolic level. In the second part of the talk\
, I describe a phase field model of a resident flu
id being displaced by injected air in a thin tube
(a microscopic pore). PDE simulations reveal the
appearance of a rarefaction wave together with a f
aster undercompressive wave that terminates at the
spherical cap tip of the injected air. Prelimina
ry analysis and ODE simulations help to explain th
is structure.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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