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

作者：Thuburn J^*; Cotter C J; Dubos T

来源：Geoscientific Model Development, 2014, 7(3): 909-929.

DOI：10.5194/gmd-7-909-2014

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. %26lt;br%26gt;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 del x del, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. %26lt;br%26gt;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.

• 出版日期2014