A Discontinuous Galerkin Transport Scheme on the Cubed Sphere

Abstract

A conservative transport scheme based on the discontinuous Galerkin (DG) method has been developed for the cubed sphere. Two different central projection methods, equidistant and equiangular, are employed for mapping between the inscribed cube and the sphere. These mappings divide the spherical surface into six identical subdomains, and the resulting grid is free from singularities. Two standard advection tests, solid-body rotation and deformational flow, were performed to evaluate the DG scheme. Time integration relies on a third-order total variation diminishing (TVD) Runge–Kutta scheme without a limiter. The numerical solutions are accurate and neither exhibit shocks nor discontinuities at cube-face edges and vertices. The numerical results are either comparable or better than a standard spectral element method. In particular, it was found that the standard relative error metrics are significantly smaller for the equiangular as opposed to the equidistant projection.