Transformed flux-form semi-Lagrangian schemes for coastal ocean modeling

Abstract

Numerical approaches in atmospheric and oceanic modeling inevitably introduce diffusion (or dissipation) and dispersion into the approximate solution. From a physical point of view, advection of a passive tracer is the simple transition of a quantity. Therefore, dispersion, the propagation of different spatial scales at different phase speed, and diffusion are processes that are aliens to the process that is being modeled (Chu and Fan 1998, 1999). As applied to constituent advection problem, these numerical artifacts manifest themselves as nonphysical mixing by numerical diffusion, nonphysical highs and lows in the constituent field caused by dispersion, and nonphysical tracer spectra caused by the trapping of tracer in nonpropagating small spatial scales (Rood 1987). The less the numerical diffusion and dispersion errors, the better the model performance is.