Finite-volume transport on various cubed-sphere grids

The performance of a multidimensional finite-volume transport scheme is evaluated on the cubed-sphere geometry. Advection tests with prescribed winds are used to evaluate a variety of cubed-sphere projections and grid modifications including the gnomonic and conformal mappings, as well as two numerically generated grids by an elliptic solver and spring dynamics. We explore the impact of grid non-orthogonality on advection tests over the corner singularities of the cubed-sphere grids, using some variations of the transport scheme, including the piecewise parabolic method with alternative monotonicity constraints. The advection tests revealed comparable or better accuracy to those of the original latitudinal–longitudinal grid implementation. It is found that slight deviations from orthogonality on the modified cubed-sphere (quasi-orthogonal) grids do not negatively impact the accuracy. In fact, the more uniform version of the quasi-orthogonal cubed-sphere grids provided better overall accuracy than the most orthogonal (and therefore, much less uniform) conformal grid. It is also shown that a simple non-orthogonal extension to the transport equation enables the use of the highly non-orthogonal and computationally more efficient gnomonic grid with acceptable accuracy.