W. Hundsdorfer et Ej. Spee, AN EFFICIENT HORIZONTAL ADVECTION SCHEME FOR THE MODELING OF GLOBAL TRANSPORT OF CONSTITUENTS, Monthly weather review, 123(12), 1995, pp. 3554-3564
In this paper the authors consider a dimensional-splitting scheme for
horizontal advection on a sphere with a uniform longitude-latitude gri
d. The 1D subprocesses that arise within the splitting are solved with
an explicit finite-volume type scheme, which is made unconditionally
stable by allowing the stencil to vary with tile Courant numbers. The
scheme is made positive by flux limiting. For the inaccuracies at the
poles some special measures are discussed. Numerical tests show that t
he scheme is almost shape preserving and conservative, and it gives ac
curate results at low computational costs.