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CUBED-SPHERE FINITE-VOLUME DYNAMICAL CORE (FVCORE)
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The finite-volume dynamical core (fvcore) is being implemented on
the quasi-uniform cubed-sphere grid within a flexible modeling framework
for direct implementation as a modular component within the global
modeling efforts at NASA, GFDL-NOAA, NCAR, DOE and other interested
institutions. The fvcore is an integral component within the NASA Goddard
Earth Observing System (GEOS) modeling suite, as well as the global
modeling efforts at GFDL and the Community Atmosphere Model (CAM) at
NCAR. The development of a cubed-sphere version of the fvcore will
expose a new level of parallelism (2-dimensional X-Y domain decomposition)
that is not feasible within the current latitude-longitude (lat-lon)
version, and allow for implementation of the purely flux-form algorithm
at a massively parallel level on a variety of computational platforms.
The cubed-sphere grid is a projection of a cube onto a sphere represented as
six adjoining grid faces which cover the globe. The cubed-sphere provides a quasi-uniform
resolution, which offers several benefits over the standard lat-lon grid currently
implemented within the fvcore. The quasi-uniform nature of the cubed-sphere grid
eliminates the parallelization difficulties associated with the poles, allowing
a far more efficient implementation of the horizontal 2-D domain decomposition,
a feature that will be required of a truly scalable ultra-high resolution earth
system model. Further, the clustering of grid points at the poles on the lat-lon
grid requires special attention to avoid violating the Courant Friedrichs-Levy
(CFL) stability requirements without dramatically reducing the integration time
step. In particular, the flux-form transport algorithm applied within the lat-lon
implementation requires a semi-lagrangian extension to allow the use of large
time steps, and a polar filter is required to stabilize the high frequency gravity
waves generated at high latitudes. The quasi-uniform nature of the cubed-sphere
grid eliminates these problems at the poles and also allows for a reasonable
time step within CFL limits without the need to extend the flux-form algorithm
and without the use of a polar filter. In addition, the cubed-sphere can be implemented
without significant algorithmic modifications and can be applied to support both
the cubed-sphere and lat-lon grids within the same code using the same flux-form
transport algorithm, a highly desirable feature as the popularity of the fvcore
continues to grow within the modeling community.
The cubed-sphere grid is ideal for 2-dimensional domain decomposition in the
X-Y direction; this is perhaps the most attractive feature of the cubed-sphere
grid. While the pole problems associated with the lat-lon grid pose significant
restrictions on the ability to impose 2-dimensional domain decomposition, this
is a rather straight forward ghosting problem with the cubed-sphere. The ability
to decompose in the X-Y direction provides great promise for producing a modeling
system scalable to 100,000s of processors. On a system such as 'Halem' (a 1388
processor Compaq AlphaServer SC45 at the NASA Center for Computational Sciences
at Goddard Space Flight Center) which supports the use of 4 shared memory processors
for each of the 347 nodes the 0.25 degree cubed-sphere grid would allow the use
of up to 345,600 processors in a hybrid message-passing/shared-memory configuration,
as opposed to 960 processors for the current latitude decomposed fvGCM. As grid
resolution is increased to 0.1 degrees the cubed-sphere would have the potential
to use up to 2,000,000+ processors on a shared memory platform like the SGI Altix
cluster 'Columbia' at the NASA Advanced Computing Division. Of course, efficient
computing on such an immense scale will demand a great deal from the hardware
in particular the interconnects between nodes; however, having the capability
to utilize 100,000s of processors will be essential for timely execution of real-time
numerical weather prediction systems with horizontal resolutions at and beyond
the hydrostatic limit (~10 km horizontal resolution).
