Numerical Method 



Due to their relative simplicity and ease of resolving complex physical 

 phenomena, finite difference models have been widely used in the study of 

 coastal currents. The finite-element method (based on the Galerkin 

 technique), despite its ability to resolve complex geometry in the 

 computational domain, has several disadvantages: (1) It is relatively more 

 complicated and expensive to program, particularly for additional nonlinear 

 terms; (2) It requires relatively more computational effort per time step; 

 and (3) It is not well suited for problems exhibiting highly-localized 

 effects such as sharp density gradients across a coastal front or a 

 thermocline. The spectral method, while considered to possess superior 

 accuracy, has the same basic disadvantages as the finite-element method. 

 Recent advancement in the numerical generation of boundary-fitted coordinates 

 has added further flexibility to the finite difference method, thus making it 

 the optimum method for simulation of coastal currents. 



Spatial Dimension 



Due to the limitation in computer resources, earlier numerical models 

 generally resolved only one or two spatial dimensions. One-dimensional models 

 are widely used for simple parametric studies and are often amenable to 

 analytic solutions. They have been used to study tidal currents and 

 water-quality parameters in estuaries (e.g., Harleman, 1975). The so-called 

 link-node model (e.g., Pagenkopf, et al . , 1977) is actually based on the 

 superposition of one-dimensional models. 



Two-dimensional models are relatively easy to use and may provide 

 reasonable answers when flow in the third dimension is relatively homogeneous. 

 Among the various types of two-dimensional models listed in Table 2.1, the 

 most widely used is probably the vertically-integrated model, which is 

 obtained by integrating the three-dimensional equations of motion in the 

 vertical direction. It has been used extensively for simulating tides, storm 

 surges, and pollutant transport in coastal environments (e.g., Leendertse, 

 1970; Butler, 1980). Due to the lack of vertical resolution, however, the 

 vertically-integrated models are not adequate for studying such problems as 

 wind-driven currents and sediment transport in coastal waters. More recently. 



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