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| Titel |
A high-order conservative collocation scheme and its application to global shallow-water equations |
| VerfasserIn |
C. Chen, X. Li, X. Shen, F. Xiao |
| 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 ; 8, no. 2 ; Nr. 8, no. 2 (2015-02-10), S.221-233 |
| Datensatznummer |
250116107
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| Publikation (Nr.) |
 copernicus.org/gmd-8-221-2015.pdf |
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| Zusammenfassung |
In this paper, an efficient and conservative collocation method is proposed and used to
develop a global shallow-water model. Being a nodal type
high-order scheme, the present method solves the pointwise values of
dependent variables as the unknowns within each control volume. The solution
points are arranged as Gauss–Legendre points to achieve high-order
accuracy. The time evolution equations to update the unknowns are derived
under the flux reconstruction (FR) framework (Huynh, 2007). Constraint
conditions used to build the spatial reconstruction for the flux function
include the pointwise values of flux function at the solution points, which
are computed directly from the dependent variables, as well as the numerical
fluxes at the boundaries of the computational element, which are obtained as
Riemann solutions between the adjacent elements. Given the reconstructed
flux function, the time tendencies of the unknowns can be obtained directly
from the governing equations of differential form. The resulting schemes have
super convergence and rigorous numerical conservativeness.
A three-point scheme of fifth-order accuracy is presented and analyzed in
this paper. The proposed scheme is adopted to develop the global
shallow-water model on the cubed-sphere grid, where the local high-order
reconstruction is very beneficial for the data communications between
adjacent patches. We have used the standard benchmark tests to verify the
numerical model, which reveals its great potential as a candidate formulation
for developing high-performance general circulation models. |
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