A conservative semi-Lagrangian discontinuous Galerkin method for transport equation on the cubed-sphere [video]
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The discontinuous Galerkin (DG) method is becoming increasingly popular in atmospheric and ocean modeling. However, a major drawback of method is its stringent CFL stability restriction associated with explicit time-stepping, e.g. explicit Runge-Kutta method. In order to get around this issue we adopt a dimension-splitting approach where a regular semi-Lagrangian (SL) scheme is combined with the DG method. The resulting SLDG scheme employs a sequence of 1D operations for solving transport equation on the cubed-sphere. 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.