TITLE:
A Semi-Lagrangian Type Solver for Two-Dimensional Quasi-Geostrophic Model on a Sphere
AUTHORS:
Quanyong Zhu, Yan Yang
KEYWORDS:
Quasi-Geostrophic Equations, Semi-Lagrangian Methods, Smoothing Technique, Error Analysis, Pole Singularity
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.18,
December
2,
2016
ABSTRACT: In thispaper, 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.