A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids
Résumé
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 discretiza-tion 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 algo-rithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equian-gular cubed-sphere grids. Results of a variety of tests are presented, including con-vergence of the discrete scalar Laplacian and Coriolis oper-ators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results con-firm a number of desirable properties for which the scheme was designed: exact mass conservation, very good avail-able energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of bal-ance 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 Cori-olis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evi-dence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.
Domaines
Sciences de la Terre
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