A Conservative Semi - Lagrangian Discontinuous Galerkin Scheme 1 on the Cubed - Sphere

6 The discontinuous Galerkin (DG) methods designed for hyperbolic problems arising from a 7 wide range of applications are known to enjoy many computational advantages. DG methods 8 coupled with strong-stability preserving explicit Runge-Kutta time discretizations (RKDG) 9 provide a robust numerical approach suitable for geoscience applications including atmo10 spheric modeling. However, a major drawback of the RKDG method is its stringent CFL 11 stability restriction associated with explicit time-stepping. In order to address this issue, we 12 adopt a dimension-splitting approach where a semi-Lagrangian (SL) time stepping strategy 13 is combined with the DG method. The resulting SLDG scheme employs a sequence of 1-D 14 operations for solving multi-dimensional transport equations. The SLDG scheme is inher15 ently conservative and has the option to incorporate a local positivity-preserving filter for 16 tracers. A novel feature of the SLDG algorithm is that it can be used for multi-tracer trans17 port for global models employing spectral-element grids, without using an additional finite18 volume grid system. The quality of the proposed method is demonstrated via benchmark 19 tests on Cartesian and cubed-sphere geometry which employs non-orthogonal, curvilinear 20 coordinates. 21