Numerical Analysis and Scientific Computing Preprint Seria 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-stability preserving explicit Runge-Kutta time discretizations (RKDG) provide a robust numerical approach suitable for geoscience applications including atmospheric modeling. However, a major drawback of the RKDG method is its stringent CFL stability restriction associated with explicit time-stepping. In order to address this issue, we adopt a dimension-splitting approach where a semi-Lagrangian (SL) time stepping strategy is combined with the DG method. The resulting SLDG scheme employs a sequence of 1-D operations for solving multi-dimensional 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 SLDG algorithm is that it can be used for multi-tracer transport for global models employing spectral-element grids, without using an additional finite-volume grid system. The quality of the proposed method is demonstrated via benchmark tests on Cartesian and cubed-sphere geometry which employs non-orthogonal, curvilinear coordinates. Department of Mathematics, University of Houston, Houston, TX 77024 National Center for Atmospheric Research, Boulder, CO 80305 Corresponding author. Department of Mathematics, University of Houston, Houston, TX, 77024,USA. E-mail: [email protected]