Discontinuous Galerkin transport on the spherical Yin-Yang overset mesh

The Yin-Yang grid is a quasi-uniform overset mesh comprising two notched latitude-longitude meshes placed at right angles to each other. Surface fluxes of conserved scalars are obtained at the overset boundaries by interpolation from the interior of the elements on the complimentary grid, using high-order polynomial interpolation intrinsic to the DG technique.

A series of standard tests are applied to evaluate its performance, revealing it to be robust and its accuracy to be competitive with other global advection schemes at equivalent resolutions. Under p-type grid refinement, the DG Yin-Yang method exhibits spectral error convergence for smooth initial conditions and third-order geometric convergence for C1 continuous functions. In comparison with finite-volume implementations of the Yin-Yang mesh, the DG implementation is less complex, as it does not require a wide halo region of elements for accurate boundary value interpolation.