Mathematics Colloquia and Seminars

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Description

We present a novel approach to modeling the dynamics of free boundaries in a flow: A thin, body-fitted grid conforms to the evolving interface, while most of the domain is covered with a fixed, Cartesian mesh. At each time step, these component grids are used to generate an overset mesh using the Overture framework. We'll consider the evolution of an air bubble displacing a non-Newtonian fluid in the prototypical thin film device, the Hele-Shaw cell. The dynamics is governed by a generalization of Darcy's law in the bulk fluid, and by the Laplace-Young condition at the fluid/gas interface. We'll discuss the numerical simulation of this problem, and also an asymptotic analysis of the flow near the meniscus. Time permitting, I'll discuss ongoing work on modeling the recent experiments of Zhang, Childress, Libchaber and Shelley on a 1D flapping flag in a two dimensional wind. (This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.)

(Refreshment is served in 693 Kerr at 1:45pm)