= U r l + At I- — K — 6 

 m+1/2 I y Aa, 2a, V / \i Aa_ 2< 



x 1 1 



(jf) _ *L 6 (u r ) 

 O. \ / p Aa 2a \ / 



y~~2 2 



- -4- « (n r_1 )- — -4- « (s r )+ tV «, fc ) 



M x Aa l °]\ } pd V°l "iW 2U y Aa 2 2a 2\ Xy / 



+ 2e 



1 1 



x Uy u x Aa 2 A ai ^ 



6 W r )+ 2e 



a„a, v ' y 



- — tt 6 (u r ) (44) 



Aa„\ 2 a 2 a 2 V J 



("y^) 



U x U y Aa^ 2a 2 \^ x y a^ / 



►at (n, m+1/2) 



At 



ra±l/2 



,m±l/2 



= n r-l _ _At (yr-1 ^r)_ _2At_ ( r-1 gr\ 



W x A0t l a l\ ' U y ACt 2 a 2^ ' 



(45) 



at (n,m) (46) 



v r = i ( y r 1 



n, m+1/2 4 V n-l/2,m n+l/2,m n-l/2,m+l n+l/2,m+li' 



36. Consider the set of cells for which the index n is constant and 

 equal to N . Suppose at the upper boundary cell (m = M) , the velocity 

 U 1 .. is always known. Similarly, suppose at the lower boundary cell 

 (m = L) the water level n N T is always known. Then the set of equations for 

 all the cells can be written in the following matrix form if the common sub- 

 script N is dropped: 



28 



