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dc.contributor.authorRingler, T.D.
dc.contributor.authorThuburn, John
dc.contributor.authorKlemp, J.B.
dc.contributor.authorSkamarock, W.C.
dc.date.accessioned2013-05-15T11:54:04Z
dc.date.issued2010
dc.description.abstractA numerical scheme applicable to arbitrarily-structured C-grids is presented for the nonlinear shallow-water equations. By discretizing the vector-invariant form of the momentum equation, the relationship between the nonlinear Coriolis force and the potential vorticity flux can be used to guarantee that mass, velocity and potential vorticity evolve in a consistent and compatible manner. Underpinning the consistency and compatibility of the discrete system is the construction of an auxiliary thickness equation that is staggered from the primary thickness equation and collocated with the vorticity field. The numerical scheme also exhibits conservation of total energy to within time-truncation error. Simulations of the standard shallow-water test cases confirm the analysis and show convergence rates between 1st1st- and 2nd2nd-order accuracy when discretizing the system with quasi-uniform spherical Voronoi diagrams. The numerical method is applicable to a wide class of meshes, including latitude–longitude grids, Voronoi diagrams, Delaunay triangulations and conformally-mapped cubed-sphere meshes.en_GB
dc.identifier.citationVol. 229 (9), pp. 3065 - 3090en_GB
dc.identifier.doi10.1016/j.jcp.2009.12.007
dc.identifier.urihttp://hdl.handle.net/10871/9404
dc.language.isoenen_GB
dc.publisherElsevieren_GB
dc.relation.urlhttp://dx.doi.org/10.1016/j.jcp.2009.12.007en_GB
dc.subjectC-griden_GB
dc.subjectVoronoi diagramen_GB
dc.subjectPotential vorticityen_GB
dc.subjectShallow-water equationsen_GB
dc.titleA unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-gridsen_GB
dc.typeArticleen_GB
dc.date.available2013-05-15T11:54:04Z
dc.identifier.issn0021-9991
dc.descriptionCopyright © 2010 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational Physics, Vol. 229, Issue 9 (2010), DOI: 10.1016/j.jcp.2009.12.007en_GB
dc.identifier.journalJournal of Computational Physicsen_GB


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