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SUMMARY:Particle methods for geophysical flow on the sphere - Peter Bosler
 \,   (University of Michigan)
DTSTART:20120925T144500Z
DTEND:20120925T151000Z
UID:TALK40088@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We develop a fluid dynamics solver for spherical domains based
  on the Lagrangian form of the equations of motion and a tree-structured m
 esh of fluid particles. Initial discretizations are based on the cubed sph
 ere or icosahedral triangles\, but these arrangements distort as the parti
 cles move with the fluid velocity. A remeshing scheme based on interpolati
 on of the Lagrangian parameter is applied at regular intervals to maintain
  computational accuracy as the flow evolves. Ongoing work with adaptive me
 sh refinement is introduced. We present solutions of the advection equatio
 n with prescribed velocities from recent test cases (Nair and Lauritzen\, 
 2010)\, and solutions of the barotropic vorticity equation where velocity 
 is given by an approximate Biot-Savart integral and midpoint rule quadratu
 re for test cases including Rossby-Haurwitz waves and Gaussian vortices . 
 The discrete equations in the barotropic vorticity equation are those of p
 oint vortices on the sphere (e.g. Bogo molov\, 1977). For the shallow wate
 r equations\, we must also include the effects of point sources upon the f
 luid particles\; we discuss the challenges posed by divergent flows in thi
 s Lagrangian context and strategies for evaluating nonlinear forcing terms
  on irregular meshes.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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