A Conservative Semi-Lagrangian Discontinuous Galerkin Scheme on the Cubed Sphere

The discontinuous Galerkin (DG) methods designed for hyperbolic problems arising from a wide range of applications are known to enjoy many computational advantages. DG methods coupled with strong-stabilitypreserving explicitRunge–Kutta discontinuousGalerkin (RKDG) timediscretizations provide a robust numerical approach suitable for geoscience applications including atmosphericmodeling.However, amajor drawback of the RKDGmethod is its stringent Courant–Friedrichs–Lewy (CFL) stability restriction associated with explicit time stepping. To address this issue, the authors adopt a dimension-splitting approach where a semi-Lagrangian (SL) time-stepping strategy is combined with the DGmethod. The resulting SLDG scheme employs a sequence of 1D operations for solving multidimensional transport equations. The SLDG scheme is inherently conservative and has the option to incorporate a local positivity-preserving filter for tracers. A novel feature of the SLDGalgorithm is that it can be used formultitracer transport for globalmodels employing spectral-element grids, without using an additional finite-volume grid system. The quality of the proposedmethod is demonstrated via benchmark tests on Cartesian and cubed-sphere geometry, which employs nonorthogonal, curvilinear coordinates.