Artificial diffusion in the numerical modelling of the advective transport of salinity

Numerical modelling of the advective transport of salinity in coastal seas, using upstream differences, is considered. Upstream differences do not give rise to spurious negative salinities, as do forward time centred space differences.It is shown that the artificial diffusion associated with upstream differences can be incorporated into the physical diffusion in a simple quantitative manner. The method is applicable to finite-difference grids of less than about 2-4 km in tidal problems. For non-tidal problems the method is applicable to larger grids.