Cubed-Sphere finite-volume dynamical core (fvcore) Overview
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).
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