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| Titel |
A global finite-element shallow-water model supporting continuous and discontinuous elements |
| VerfasserIn |
P. A. Ullrich |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1991-959X
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| Digitales Dokument |
URL |
| Erschienen |
In: Geoscientific Model Development ; 7, no. 6 ; Nr. 7, no. 6 (2014-12-17), S.3017-3035 |
| Datensatznummer |
250115798
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| Publikation (Nr.) |
 copernicus.org/gmd-7-3017-2014.pdf |
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| Zusammenfassung |
| This paper presents a novel nodal finite-element method for either continuous
and discontinuous elements, as applied to the 2-D shallow-water equations on
the cubed sphere. The cornerstone of this method is the construction of a
robust derivative operator that can be applied to compute discrete
derivatives even over a discontinuous function space. A key advantage of the
robust derivative is that it can be applied to partial differential equations
in either a conservative or a non-conservative form. However, it is also
shown that discontinuous penalization is required to recover the correct
order of accuracy for discontinuous elements. Two versions with discontinuous
elements are examined, using either the g1 and g2 flux correction
function for distribution of boundary fluxes and penalty across nodal points.
Scalar and vector hyperviscosity (HV) operators valid for both continuous and
discontinuous elements are also derived for stabilization and removal of
grid-scale noise. This method is validated using four standard shallow-water
test cases, including geostrophically balanced flow, a mountain-induced
Rossby wave train, the Rossby–Haurwitz wave and a barotropic instability.
The results show that although the discontinuous basis requires a smaller
time step size than that required for continuous elements, the method
exhibits better stability and accuracy properties in the absence of
hyperviscosity. |
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