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SUMMARY:Mimetic Semi-implicit Solution of the Shallow Water Equations on H
 exagonal-Icosahedral and Cubed-Sphere Grids - John Thuburn\,   (University
  of Exeter)
DTSTART:20120924T093000Z
DTEND:20120924T095500Z
UID:TALK40011@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A new algorithm is presented for the solution of the shallow w
 ater equations on quasi-uniform spherical grids. It combines a mimetic spa
 tial discretization with a Crank-Nicolson time scheme for fast waves and a
 n accurate and conservative forward-in-time advection scheme for mass and 
 potential vorticity. The algorithm is tested on two families of grids: hex
 agonal-icosahedral Voronoi grids\, and modified equiangular cube-sphere gr
 ids. For the cubed-sphere case\, a key ingredient is the development of a 
 suitable discrete Hodge star operator for the non-orthogonal grid. \n\nRes
 ults of several test cases will be presented. The results confirm a number
  of desirable properties for which the scheme was designed: exact mass con
 servation\, very good available energy and potential enstrophy conservatio
 n\, vanishing curl of grad\, steady geostrophic modes\, and accurate PV ad
 vection. The scheme is stable for large wave Courant numbers and for advec
 tive Courant numbers up to about one. \n\nThe accuracy of the scheme appea
 rs to be limited by the accuracy of the various mimetic spatial operators.
  On the hexagonal grid there is no evidence for damaging effects of comput
 ational Rossby modes\, despite attempts to force them explicitly.\n
LOCATION:Seminar Room 1\, Newton Institute
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