the transport rate must be specified at the boundaries, Q x and Q N+1 , and 

 the remainder of the Q i and all y t will be calculated. Since the Q L are 

 a function of the wave conditions, all wave quantities are calculated at Q- 

 points . The tips of structures are likewise located at Q-points. Beach 

 fills, river discharges, and other sand sources and sinks are located at y- 

 points. 



1-1 i i+1 



DISTANCE ALONGSHORE/GRID CELL NUMBER 



Figure 18. Finite difference staggered grid 



Implicit finite difference solution scheme 



176. In the following, a subscript i denotes a quantity located at an 

 arbitrary cell number i along the beach. A prime (') is used to denote a 

 quantity at the new time level, whereas an unprimed quantity indicates a value 

 at the present time step, which is known. The quantities y' and Q' are 

 not known and are being sought in the solution process; other primed quan- 

 tities such as q' and Dg refer to data at the next time step and are known. 



85 



