Note on the choice of geographic propagation schemes

The main interest of the SWAN users is in simulating wind-generated waves and combined swell-sea cases in coastal ocean waters, and it is particularly with the view to such computations that a simple and compact, but first order BSBT scheme was implemented in SWAN. A substantial body of experience gathered over the past 20 years on the performance of both lower and higher upwind schemes in SWAN suggests that in many circumstances, the discretization of the propagation terms in geographical space is not a crucial issue. Many nearshore simulations have shown the solution for action density to be on the whole rather insensitive to the accuracy with which geographic propagation terms are approximated. This reflects the tendency for the level of wave action to be dictated by source terms, while the local changes of the energy field across geographical space is relatively weak. This is consonant with the established view that a certain amount of numerical diffusion can be safely tolerated in the numerical scheme for geographic propagation, as its impact on wave parameters is negligible (Rogers et al., 2002; WISE Group, 2007). Also, broad wave spectra will tend make numerical diffusion far less noticeable in a wave field.


This would appear to suggest, however, that the use of higher order upwind schemes serves no useful purpose. This is probably not so since there might be some cases that are prone to diffusion, where the benefit of such schemes is obvious. One can think of a case of swell propagation over very long distances. While low-diffusive, higher order schemes did permit long-distance swell cases to be validated, the reduced diffusion was found to pose a serious difficulty as the garden sprinkler effect becomes more visible, see e.g. WISE Group (2007).