A unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-grids

A 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 1st- and 2nd-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.

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Copyright 2010 Author(s). NOTICE: This is the author's version of a work submitted for publication by Elsevier. Changes resulting from the publishing process, including 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.


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Author Ringler, T.
Thuburn, J.
Klemp, Joseph
Skamarock, William
Publisher UCAR/NCAR - Library
Publication Date 2010-04-01T00:00:00
Digital Object Identifier (DOI) Not Assigned
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Topic Category geoscientificInformation
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Metadata Date 2023-08-18T19:05:59.268336
Metadata Record Identifier edu.ucar.opensky::articles:18104
Metadata Language eng; USA
Suggested Citation Ringler, T., Thuburn, J., Klemp, Joseph, Skamarock, William. (2010). A unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-grids. UCAR/NCAR - Library. http://n2t.net/ark:/85065/d7251krr. Accessed 15 February 2025.

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