A Fourier finite volume element method for solving two-dimensional quasi-geostrophic equations on a sphere

A new Fourier finite volume element method for solving quasi-geostrophic (QG) equations on a sphere has been developed in this paper. Using the spherical coordinates, a Fourier discretization is used in the longitudinal direction while a finite volume element approximation is used in the latitudinal direction. In our proposed numerical method, the trial and test function spaces are carefully chosen to get accurate approximations. The pole singularity associated with the spherical coordinates is eliminated by changing the resolution near the pole. Some numerical experiments are presented to illustrate accuracy and efficiency of our method and some geostrophic implications of the QG model.