A Semi-Lagrangian Discontinuous Galerkin (SLDG) Conservative Transport Scheme on the Cubed-Sphere
Seminar Room 1, Newton Institute
AbstractThe discontinuous Galerkin (DG) method combines fine features of high-order accurate finite-element and finite-volume methods. Because of its geometric flexibility and high parallel efficiency, DG method is becoming increasingly popular in atmospheric and ocean modeling. However, a major drawback of DG method is its stringent CFL stability restriction associated with explicit time-stepping. A way to get around this issue is to combine DG method with a Lagrangian approach based on the characteristic Lagrange-Galerkin philosophy. Unfortunately, a fully 2D approach combining DG and Lagrangian methods is algorithmically complex and computationally expensive for practical application, particularly for non-orthogonal curvilinear geometry such as the cubed-sphere grid system. 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 (structured or unstructured) grids. The SLDG scheme is tested for various benchmark advection test-suites on the sphere and results will be presented in the seminar.
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