impossible to achieve such a low error level in simulating complex coastal 

 currents due to uncertainties in model parameters and numerical errors from 

 other terms, implementation of a complex fourth-order scheme to numerical 

 hydrodynamic models does not appear to be justified. 



A flux-corrected transport (FCT) method, suitable for simulating flow 

 situations involving discontinuities and sharp gradients (e.g., Shockwave, 

 thermocline, front), has been developed by the NRL group (Boris and 

 Book, 1976; Zalesak, 1979). This is a two-step method based on the 

 combination of a lower-order advective scheme (with relatively high numerical 

 diffusion but little numerical dispersion) and a higher-order scheme (with 

 little damping but higher numerical dispersion). In the first step, a lower 

 order calculation is performed. A higher-order scheme is then applied to 

 compute the advective fluxes and the "anti-diffusive fluxes", i.e., the 

 differences between the higher-order and the lower-order fluxes. The second 

 step, a corrective step, adds a limited amount of anti-diffusive fluxes to the 

 lower-order solution such that the new solution is free of overshoots or 

 undershoots. The FCT algorithm was able to accurately resolve shocks and 

 sharp gradients with no apparent penalty in regions where they are absent. 

 Using the second upwind scheme as the lower-order scheme and a second-order 

 scheme as the higher-order scheme, this FCT scheme has been applied to 

 simulate the transport of a concentrated patch of passive contaminant by 

 wind-driven currents in an idealized basin (Sheng, 1981) and was found to 

 yield much better results than the one-step results of a lower-order scheme or 

 a higher-order scheme. This study is included in Appendix E. 



50 



