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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Michael Shearer
North Carolina State University
Title: Two Phase Flow in Porous Media: the Saffman-Taylor Instability Revisited

Abstract: Plane waves for two phase flow in a porous medium are modeled by the one-dimensional Buckley-Leverett equation, a * scalar* conservation law. We analyze linearized stability of sharp planar interfaces to two-dimensional perturbations, which involves a * system* of PDE. Numerical simulations of the full nonlinear system, including dissipation, illustrate the analytical results. We also discuss a modified Buckley-Leverett equation, in which the capillary pressure is rate-dependent, thereby adding a BBM-type dispersive term. This equation sustains undercompressive planar waves, but they are all unstable to two-dimensional perturbations.This is joint work with Kim Spayd and Zhengzheng Hu.

Recording: http://vnc.math.cmu.edu/cna/CNA-Shearer-Oct-27-2011.avi
Recording: http://vnc.math.cmu.edu/cna/CNA-Shearer-Oct-27-2011.mp4
Date: Thursday, October 27, 2011
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  David Kinderlehrer