Article citationsMore>>

Amato, U. and Carfora, M. (2000) Semi-Lagrangian Treatment of Advection on the Sphere with Accurate Spatial and Temporal Approximations. Mathematical and Computer Modelling, 32, 981-995.
https://doi.org/10.1016/S0895-7177(00)00184-9

has been cited by the following article:

• 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.