Implementation of a Semi-Lagrangian Scheme in the Tracer Transport Equation on a Cubed-Sphere Grid
Abstract
In order to enhance positive-definite and shape-preserving properties of the Eulerian-type spectral element transport scheme, a semi-Lagrangian scheme have been tried to implement in a global atmospheric spectral element model on a cubed-sphere grid. The scheme avoids complex and expensive upstream area computations on the finite-volume grid (equi-distant cell grid). Since the spectral element model is based on the Gaussian-Legendre-Lobatto (GLL) grid, the semi- Lagrangian scheme includes two different grids such as the finite-volume grid and the GLL grid, involving an interpolation operator of piecewise continuous functions to interchange. Through the comparisons of error norms between the numerical experiments using the semi-Lagrangian scheme and Eulerian-type spectral element scheme, they are observed that the proposed scheme is more accurate than the spectral element scheme of Eulerian-type in the high-resolution meshes. It is prominent for the non-smooth test case.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2018
- Bibcode:
- 2018AGUFMNG31A0926N
- Keywords:
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- 3225 Numerical approximations and analysis;
- MATHEMATICAL GEOPHYSICSDE: 4455 Nonlinear waves;
- shock waves;
- solitons;
- NONLINEAR GEOPHYSICSDE: 4490 Turbulence;
- NONLINEAR GEOPHYSICSDE: 7524 Magnetic fields;
- SOLAR PHYSICS;
- ASTROPHYSICS;
- AND ASTRONOMY