2.5 Lateral Grid Resolution 



Earlier models of global ocean or lake circulations generally used a 

 relatively coarse uniform rectangular grid in the horizontal direction of the 

 computational domain. However, complex shoreline and bottom topography and 

 Islands often exist in a lake or coastal environment. To better resolve the 

 shoreline geometry and internal features, and additionally allow proper 

 coupling between the various regions of a coastal environment, a smoothly 

 varying non-uniform grid can be used. As shown in Figure 2.2, a non-uniform 

 horizontal grid in the real space {x,y) is mapped into a uniform horizontal 

 grid in the computational space {a,T) by the following piecewise reversible 

 transformations: 



X = a^ + hya ^ , y = By + b^y y (2.22) 



where a^^, b^^, Cj^, ay, by and Cy are user-specified stretching coefficients 

 (Appendix B). By applying a smoothly varying grid transformation, whose 

 functional as well as first derivatives are continuous, many stability 

 problems commonly associated with variable grid schemes are eliminated 

 provided that all derivatives are centered in the stretched system (a,Y,o). 



This lateral stretching does not add any extra terms to the equations of 

 motion, although the stretching coefficients as defined by Mj(=da/dx and 

 jiy=dY/dy now appear in all of the spatial derivative terms. 



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