with jj = v = 1, and 



F(i,j) 



IT 



88 



r ri 



+ 



Cj - 



2)2 



AT*.." 



i 





AS* 





J 



i 



- i 



2 





45 



> 



J 



- 2 



3 





22 





(91) 



where AS* = 21.05 kilometers and AT* = 19.65 kilometers. Approxi- 

 mately the same number of computational points are employed in this 

 system as that of Figure 51. The actual area of the annulus is well 

 represented in both computing grids. Although the inner and outer 

 boundaries are straight-line segments in the numerical grid sense, 

 the portrayal of the annulus is certainly more representative than 

 that shown in Figure 51. The positions of nine hydrographs in 

 Figure 52 (denoted by large dots) correspond to the hydrograph posi- 

 tions in the rectilinear grid system. For the polar system, the 

 maximum numerical time step is approximately 600 seconds. As a 

 practical note, the stretched shelf coordinate system, although re- 

 quiring less sophisticated programing and allowing better physical 

 and mathematical portrayal of the boundaries, generally results in 

 a smaller numerical time step than a rectilinear system of comparable 

 scale. 



2. Results . 



For comparison purposes, a time step of 540 seconds is used in 

 both grid systems for the numerical solution. As noted above, the 

 polar grid program should compile and execute faster on the computer 

 than the rectilinear grid program. On the IBM 360/65, the polar 

 grid program required 0.47 minute to compile and 0.39 minute per 

 100 iterations. For the rectilinear system, the program consumed 

 0.59 minute to compile and 0.61 minute per 100 iterations. 



The initial surface elevation condition which is imposed on both 

 grid systems is that 8H/38 is a constant. For the rectilinear grid 

 system, 



H(i,j,0) 



1 - 



tan 



-1 





(92) 



where only the i,j indices appropriate for the annulus are employed 

 in the above relation. For the polar grid system, the same initial 

 surface condition is determined as : 



96 



