A hydrodynamical kernel that drives both an atmospheric and oceanic
general circulation model is implemented in general orthogonal curvilinear coordinates using the finite volume method on the sphere. The finite volume method naturally describes arbitrary grids and use of the vector invariant form of the momentum equations simplifies the generalization to arbitrary
coordinates. We use grids based on the expanded spherical cube of Rancic
et al. (1996) which contain eight singular points. At these singularities the grid is non-orthogonal. The combined use of vector invariant equations and
the finite volume method is shown to avoid degeneracy at these singular
points.