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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On Time Integration and the Use of Clebsch Variabl
es in Shallow Water Equations - Bokhove\, O (Unive
rsity of Leeds)
DTSTART;TZID=Europe/London:20131206T110000
DTEND;TZID=Europe/London:20131206T114500
UID:TALK49233AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/49233
DESCRIPTION:Two topics will be covered in this lecture. The sh
allow water equations will be used as a test bed t
o introduce the ideas. \n\n(i) For forced variatio
nal systems such as the potential flow shallow wat
er wave equations\, variational and symplectic tim
e integrators will be extended using a new finite
element approach. Here\, a standard variational fi
nite element discretization will be applied in spa
ce. \n\n(ii) The shallow water equations formulate
d in terms of Clebsch variables will be discussed.
The advantage of Clebsch variables is that they l
ead to canonical Hamilton's equations for shallow
water dynamics\, in the Eulerian framework. A disa
dvantage is that the the system\, is less compactl
y expressed in comparison to the usual formulation
in terms of the velocity and fluid depth. I will
make a link between a symmetry in the Hamiltonian
and the associated mass weighted potential vortici
ty conservation law\, also within the Eulerian fra
mework. This will be done in two dimensions (2D) a
nd in a quasi-2D symmetric form. \n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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