and q in the x and y directions, respectively, and a.. and ou are coordi- 

 nates in the computational space. This transformation allows all derivatives 

 to be centered in the computational space. Many stability problems commonly 

 occurring in variable grid schemes are eliminated when using this transforma- 

 tion since the real space grid is smoothly varying with the coordinate and its 

 first derivative being continuous at the boundaries between regions. 



7. The partial differential equations are solved by finite difference 

 integration on a grid of spatial points. A right-handed coordinate system is 

 used with the x-coordinate increasing in the offshore direction and the 

 y-coordinate increasing along the shoreline with the ocean to the right. The 

 partial derivative of an arbitrary variable s in domain p is 



8s _ 1_ 9s 

 9x y 9a.. 



(3) 



where 



Similarly 



where 



* c - 1 



y = -5 — = b c a. r (4) 



x 9a p p 1 



9s _ 1__ 9s 

 9y " y 3a 2 



(5) 



y --!*-« b c a^" 1 (6) 



y 9a 2 q q 2 



If the grid in the x-, y-coordinate system is to have even grid spacing, all 



values of y and y will be constant (1 if Aa, = Ax and Aa. = Ay). The 

 x y 1 2 



constants a , b , c , a , b , and c for all the domains and the values 

 p p p q q q 



of y and y at grid cell faces and centers are determined using an 

 interactive computer program called MAPIT. 



8. Figure 2 shows the variable finite difference numerical grid used by 

 all of the numerical models presented in this report to calculate coastal and 

 inlet processes at Oregon Inlet. The grid has 4,158 cells and covers an area 

 of approximately 60 square miles with grid cells having side lengths as small 

 as 100 ft. If a uniform grid were used with 100-ft grid cells, approximately 

 170,000 grid cells would be required. Since the computational time require- 

 ments of the numerical models presented in this report generally increase with 



