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A Semi-Lagrangian Type Solver for Two-Dimensional Quasi-Geostrophic Model on a Sphere
Department of Mathematics, Lishui University, Lishui, China
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
- 1 Department of Mathematics, Lishui University, Lishui, China
- 2 Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
Applied Mathematics·Volume 07 (2016)·Pages 2296–2306·Published 2 December 2016·DOI10.4236/am.2016.718181
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Abstract
In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-order centered difference is suggested on the latitude-longitude grid. In our proposed numerical scheme, advection terms are expressed in a Lagrangian frame of reference to circumvent the CFL restriction. The pole singularity associated with the latitude-longitude grid is eliminated by a smoothing technique for the initial flow. Error analysis is provided for the numerical scheme.
KeywordsQuasi-Geostrophic EquationsSemi-Lagrangian MethodsSmoothing TechniqueError AnalysisPole Singularity
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