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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Using Data to Accurately and Efficiently Model Tur
bulent Flows: Data Assimilation &\; Parameter R
ecovery - Elizabeth Carlson (University of Victori
a)
DTSTART;TZID=Europe/London:20220301T111500
DTEND;TZID=Europe/London:20220301T121500
UID:TALK170768AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170768
DESCRIPTION:One of the challenges of the accurate simulation o
f turbulent flows is that initial data is often in
complete. Data assimilation circumvents this issue
by continually incorporating the observed data in
to the model. An emerging approach to data assimil
ation known as the Azouani-Olson-Titi (AOT) algori
thm introduced a feedback control term to the 2D i
ncompressible Navier-Stokes equations (NSE) in ord
er to incorporate sparse measurements. The solutio
n to the AOT algorithm applied to the 2D NSE was p
roven to converge exponentially to the true soluti
on of the 2D NSE with respect to the given initial
data. In this talk\, we present our tests on the
robustness\, improvements\, and implementation of
the AOT algorithm\, as well as generate new ideas
based off these investigations. First\, we discuss
the application of the AOT algorithm to the 2D NS
E with an incorrect parameter and prove it still c
onverges to the correct solution up to an error de
termined by the error in the parameters. This led
to the development of a simple parameter recovery
algorithm\, whose convergence we recently proved i
n the setting of the Lorenz equations. It has now
been proven by a co-author for the full 2D NSE\, p
resenting new insights into the equation itself. T
he implementation of this algorithm led us to prov
ide rigorous proofs that the solution to the corre
sponding sensitivity equations coincides with the
Fr{\\'e}chet derivative of the solution to the ori
ginal equations. We may also discuss nonlinear alg
orithms and applications to climate models.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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