Thursday, Nov 14, 9:30 am in MTH 3206, University of Maryland,
College Park
Computing interfacial flows with surface tension
Prof. Michael Shelley
Courant Institute,
New York University,
New York
Many fundamental problems in fluid mechanics and materials science
concern the dynamics of interfaces mediated by surface tension or
energy -- pattern and singularity formation are two important
examples. For a computational scientist, surface tension leads
to severe time-step constraints that are both nonlinear and
dynamical in nature. I will discuss an approach, based on a
"Small-Scale Decomposition", that for a class of such problems
circumvents these difficulties. By reposing the dynamics in
intrinsic coordinates, and analyzing the equations of motion
at small length-scales, the contribution of the surface tension
can be isolated as a linear term that can be treated implicitly,
which leads to efficient and accurate time-stepping methods.
These methods are illustrated through computational studies of
the effect of surface tension on the Kelvin-Helmholtz instability,
pattern formation problems in the Hele-Shaw cell, and others.
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