Conservative transport schemes for spherical geodesic grids: High-order reconstructions for forward-in-time schemes

The use of second- and fourth-order reconstructions, in contrast to the first-order reconstruction used in the original scheme, results in significantly more accurate solutions at a given mesh density, and better phase and amplitude error characteristics in standard transport tests.

The schemes using the higher-order reconstructions also exhibit much less dependence of the solution error on the time step compared to the original formulation. The original scheme of Miura was only tested using a nondeformational time-independent flow. The deformational time-dependent flow test used to examine 2D planar transport in Blossey and Durran is adapted to the sphere, and the schemes are subjected to this test.