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SUMMARY:On the way to the limit: finite epsilon effects in oscillatory flu
 id dynamics and their numerical approximation with time-parallel methods -
  Beth Wingate (University of Exeter)
DTSTART:20220518T090000Z
DTEND:20220518T100000Z
UID:TALK173561@talks.cam.ac.uk
DESCRIPTION:In highly oscillatory fluid dynamics\, such as fluids that gov
 ern Earth's atmosphere and ocean\, the role of the waves on developing and
  sustaining a mean\, low-frequency flow is an interesting question with fa
 r-reaching consequences for how we perform numerical computations. In this
  talk I will discuss the role of finite-epsilon effects from time-scale se
 parated PDEs on the formation and persistence of low-frequency phenomenon 
 and its impact on numerical time stepping methods of the future. I will re
 ly on the use of the semi-group operator as a mapping that helps reveal th
 e mathematical structure of the PDE\, and averaging\, from common techniqu
 es used in the study of fast singular limits. &nbsp\; I will give examples
  of ODEs\, and numerical computations of the shallow water equations. Fina
 lly\, I will give a friendly introduction to time-parallel time-stepping m
 ethods and sketch a new proof of convergence for the parareal method when 
 there is finite epsilon time-scale separation.
LOCATION:Seminar Room 1\, Newton Institute
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