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SUMMARY:A conservative adaptive wavelet method for the shallow water equat
 ions on staggered grids - Nicholas Kevlahan\,   (McMaster University)
DTSTART:20120924T151000Z
DTEND:20120924T153500Z
UID:TALK40014@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:This paper presents the first dynamically adaptive wavelet met
 hod for the shallow water equations on a staggered hexagonal C-grid. Press
 ure is located at the centres of the primal grid (hexagons) and velocity i
 s located at the edges of the dual grid (triangles). Distinct biorthogonal
  second generation wavelet transforms are developed for the pressure and t
 he velocity. These wavelet transforms are based on second-order accurate i
 nterpolation and restriction operators. Together with compatible restricti
 on operators for the mass flux and Bernoulli function\, they ensure that m
 ass is conserved and that there is no numerical generation of vorticity wh
 en solving the shallow water equations. Grid refinement relies on appropri
 ate thresholding of the wavelet coefficients\, allowing error control in b
 oth the quasi-geostrophic and inertia-gravity wave regimes. The shallow wa
 ter equations are discretized on the dynamically adapted multiscale grid u
 sing a mass and potential-enstrophy conserving finite-difference scheme. T
 he conservation and error control properties of the method are verified by
  applying it to a propagating inertia-gravity wave packet and to rotating 
 shallow water turbulence. Significant savings in the number of degrees of 
 freedom are achieved even in the case of rotating shallow-water turbulence
 . The numerical dissipation introduced by the grid adaptation is quantifie
 d. The method has been designed so it can be extended easily to the icosah
 edral subdivision of the sphere. This work provides important building blo
 cks for the development of fully adaptive general circulation models.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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