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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Interaction Dynamics of Singular Wave Fronts Compu
ted by Particle Methods - Alina Chertock (North Ca
rolina State University)
DTSTART;TZID=Europe/London:20220718T150000
DTEND;TZID=Europe/London:20220718T153000
UID:TALK176090AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/176090
DESCRIPTION:Some of the most impressive singular wave fronts s
een in Nature are the transbasin oceanic internal
waves\, which may be \;observed from a space s
huttle\, as they propagate and interact with each
other. The characteristic feature of these strongl
y \;nonlinear waves is that they reconnect whe
never any two of them collide transversely. The dy
namics of these internal wave \;fronts is gove
rned by the so-called EPDiff equation\, which\, in
particular\, coincides with the dispersionless ca
se of the \;Camassa-Holm (CH) equation for sha
llow water in one- and two-dimensions.In this talk
\, I will present a particle method for the numeri
cal simulation and investigation of solitary wave
structures of the EPDiff \;equation. \;I w
ill also provide global existence and uniqueness r
esults for this family of fluid transport equation
s by \;establishing convergence results for th
e particle method. The latter is accomplished by u
sing the concept of space-time bounded variation a
nd the associated compactness properties. \;\n
Finally\, I will present numerical examples that d
emonstrate the performance of the particle \;m
ethods in both one and two dimensions. The numeric
al results illustrate that the particle method has
superior features and represent huge computationa
l savings when the initial data of interest lies o
n a submanifold. The method can also be effectivel
y implemented in straightforward fashion in a para
llel computing environment for arbitrary initial d
ata.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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