Taylor, Tribbia and Iskandarni, "The spectral element method
for the shallow water equations on the sphere,"
submitted: Journal of Computational Physics, 1995


ABSTRACT


The spectral element method is implemented for the shallow
water equations in spherical geometry and its performance is
compared with other models.  This is the first step in
evaluating the suitability of spectral elements for climate
modeling.  The potential advantages and disadvantages of
spectral elements over more conventional models used for
climate studies are discussed.  The method requires that the
sphere be tiled with rectangles, for which we make use of
the gnomonic projection to map the sphere onto the cube.  To
measure the performance of the method relative to other
models, results are presented from a standard suite of
shallow water test cases for the sphere.  These results
confirm the spectral accuracy of the method.