Monday, 12 January 2004

A Finite-Volume Mass- and Vorticity-conserving Solver of the Shallow-Water Equations on the Sphere using Penta-/Hexagonal Grids

Room 4AB

**William Sawyer**, Swiss Federal Institute of Technology, Zurich, Switzerland

The motivation for this research comes from recent
work in Atmospheric General Circulation Models (AGCMs)
for NWP and climate research. The three-dimensional
Primitive Equations used in AGCMs to describe the dynamics
of the atmosphere can be decoupled [Lin,1997] into N
(number of atmospheric levels) two-dimensional shallow
water equations on the sphere. The conservation of mass and
vorticity (and thus angular momentum) is key to long term
climate simulations. Most current production AGCMs employ
orthogonal latitude-longitude grids which suffer from
numerical instabilities near the poles due to decreasing
spatial intervals. Penta-/hexagonal grids - generated,
for example, by properly subdividing a dodecahedron - do
not exhibit this deficiency and have certain technical
advantages for finite-volume methods.

We present a finite-volume scheme as well as initial
numerical simulation results, for the shallow water
model on the sphere using penta-/hexagonal grids. The
algorithm retains certain aspects of one for
latitude-longitude grids [Lin,Rood,1997]. The irregular
structure of the new grid, however, presents new challenges,
particular for the calculation of energy and geopotential
gradients and vorticity fluxes. Radial basis functions
are therefore used for the accurate and efficient
approximation of these values. The resulting algorithm
lends itself well to an implementation on parallel
supercomputers.

Rerences:

[Lin,1997] Lin, S.-J., A finite-volume integration
method for computing pressure gradient
force in general vertical coodinates,
Q. J. R. Meteorol. Soc. (1997)No. 123,
pp. 1749-1762.

[Lin,Rood,1997] Lin, S.-J., Rood, R.B., An explicit
flux-form semi-Lagrangian shallow-water
model on the sphere, Q. J. R. Meteorol.
Soc. (1997), No. 123, pp. 2477-2498.

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