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In a previous article [J. Comp. Phys. $\mathbf{357}$ (2018) 282-304], themixed mimetic spectral element method was used to solve the rotating shallowwater equations in an idealized geometry. Here the method is extended to asmoothly varying, non-affine, cubed sphere geometry. The differential operatorsare encoded topologically via incidence matrices due to the use of spectralelement edge functions to construct tensor product solution spaces in$H(\mathrm{rot})$, $H(\mathrm{div})$ and $L_2$. These incidence matricescommute with respect to the metric terms in order to ensure that the mimeticproperties are preserved independent of the geometry. This ensures conservationof mass, vorticity and energy for the rotating shallow water equations usinginexact quadrature on the cubed sphere. The spectral convergence of errors aresimilarly preserved on the cubed sphere, with the generalized Piolatransformation used to construct the metric terms for the physical fieldquantities.

A Mixed Mimetic Spectral Element Model of the Rotating Shallow Water Equations on the Cubed Sphere