Abstract: Two
fundamental problems in numerically simulating
Global Climate Models (GCMs) which have challenged
researchers during the past few decades are the
longterm stability requirements in the underlying
numerical approximations of the climate model along
with the sensitivity to small changes in regional
scales of the model. Most GCMs in the past have had
difficulty being able to simulate regional
meteorological phenomena such as tropical storms,
which play an important part in the latitudinal
transfer of energy and momentum. This is partly due
to the fact that climate models have traditionally
employed spectral methods using spherical harmonics
which are global and require excessively large
resolution in order to inherit any properties which
can be used to study regional scale phenomenon. This
is a massive computational burden since the increase
in resolution must be done globally due to the
nature of the numerical method. Furthermore,
coupling the climate model to physics forcing
packages and to data provided by remote sensing
requires local interpolation and thus the
exponential convergence of the spectral method is
lost. In this presentation, we introduce a hybrid
numerical technique that couples spectral element
approximation methods for global approximation with
a meshless collocation method developed in [Blakely
(2006)] for regional approximation for largescale
geophysical fluid problems on the sphere. The
interest in constructing such a hybrid numerical
method for largescale problems is namely to capture
the robust highorder approximation properties of
spectral element methods with the versatile
approximation properties of meshless collocation. We
demonstrate that this hybrid method allows for
highorder approximation at a global scale along
with regional approximation on smaller scales using
the meshless collocation technique without the need
for a traditional computational mesh. An efficient
parallel formulation of the hybrid method will be
presented along with numerical examples using
standard test problems of the shallowwater
equations on the sphere from Williamson et al
[Williamson et al. (1994)], validating the
robustness and accuracy of the method.
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