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SUMMARY:Interaction Dynamics of Singular Wave Fronts Computed by Particle 
 Methods - Alina Chertock (North Carolina State University)
DTSTART:20220718T140000Z
DTEND:20220718T143000Z
UID:TALK176090@talks.cam.ac.uk
DESCRIPTION:Some of the most impressive singular wave fronts seen in Natur
 e are the transbasin oceanic internal waves\, which may be&nbsp\;observed 
 from a space shuttle\, as they propagate and interact with each other. The
  characteristic feature of these strongly&nbsp\;nonlinear waves is that th
 ey reconnect whenever any two of them collide transversely. The dynamics o
 f these internal wave&nbsp\;fronts is governed by the so-called EPDiff equ
 ation\, which\, in particular\, coincides with the dispersionless case of 
 the&nbsp\;Camassa-Holm (CH) equation for shallow water in one- and two-dim
 ensions.In this talk\, I will present a particle method for the numerical 
 simulation and investigation of solitary wave structures of the EPDiff&nbs
 p\;equation.&nbsp\;I will also provide global existence and uniqueness res
 ults for this family of fluid transport equations by&nbsp\;establishing co
 nvergence results for the particle method. The latter is accomplished by u
 sing the concept of space-time bounded variation and the associated compac
 tness properties.&nbsp\;\nFinally\, I will present numerical examples that
  demonstrate the performance of the particle&nbsp\;methods in both one and
  two dimensions. The numerical results illustrate that the particle method
  has superior features and represent huge computational savings when the i
 nitial data of interest lies on a submanifold. The method can also be effe
 ctively implemented in straightforward fashion in a parallel computing env
 ironment for arbitrary initial data.
LOCATION:Seminar Room 1\, Newton Institute
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