along with assuming that the change in the denominator is small for a 

 reasonable time-step (the numerator has been averaged over the n^*^ and n + 

 ith time-steps), equation (30) results in 



where (S3)^. . = i^) (v. .) cos (2e) (2 cos a^) ^ 



(ax^ . .y2 ) 



2\l/2 



(RHSD; . = (v. .) (2 sin e cos e)(cos a - 1)-(S3). .(y" .-yj , .) 



2 

 Here it has also been assumed that cos a^ does not change over the time 



step. Equation (33) is the final form of the longshore sediment transport 



equation prior to its use in conjunction with the other equations. 



Averaging y values on the n^^^ and (n+D^I^ time-steps, equation (29) 

 can be rewritten as 



where Const5(i,j) = Coff('''J)- ^^- This is the final form on the 

 onshore-offshore sediment transport equation. 



The equation of continuity, finite-differenced for the n^^ and 

 (n+l)^*^ time-steps, can be written as 



n+1 n / \ 



At 2AXAh X. . x.^j x.^^^j x.^^^j y.^j. y.^^ y.^j^^ ^\,i^i 



^ (35) ^ 



Defining Ri^j as l/(2AXAh), inserting equations (33) and (34) into equation 

 (35), and transferring all known quantities for the n^h time-step to the 

 right-hand side of the equation result in 



24 



