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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Volume 7, issue 3
Geosci. Model Dev., 7, 909–929, 2014
https://doi.org/10.5194/gmd-7-909-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Isaac Newton Institute programme on multiscale numerics for...

Geosci. Model Dev., 7, 909–929, 2014
https://doi.org/10.5194/gmd-7-909-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.

Development and technical paper 20 May 2014

Development and technical paper | 20 May 2014

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids

J. Thuburn1, C. J. Cotter2, and T. Dubos3 J. Thuburn et al.
  • 1University of Exeter, College of Engineering, Mathematics and Physical Sciences, Exeter, UK
  • 2Imperial College, Department of Mathematics, London, UK
  • 3IPSL/Laboratoire de Météorologie Dynamique, École Polytechnique, Palaiseau, France

Abstract. A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids.

Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1.

In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

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