boundary nodes , can be readily determined from a sketch such as Figure 3 , 

 which needs to be prepared based on physical features, particularly depth 

 changes, changes in channel width, and inferred flow direction. 



45 . The purpose of DYNLETl is to determine values of flow properties at 

 all points in each channel. Selecting the flow rate or discharge Q and the 

 water surface elevation z as the basic flow variables, each node has two un- 

 knowns, the values of Q and z. If there are N nodes in the inlet system, the 

 total of number of unknowns is 2N . Therefore, 2N equations are needed to 

 determine the values of the 2N basic unknowns. These equations are obtained 

 from three sources : 



a. Application of the shallow-water equations to the interior 

 points of each channel. 



b. External boundary conditions. 



c. Junction conditions. 



46. It follows that development of a numerical model based on the one- 

 dimensional shallow-water equations for a complex inlet system consisting of 

 interconnecting channels and bays requires three types of information: 



a. Identification of interior points. 



b. Specification of external boundary conditions. 



c. Specification of junction conditions. 



Interior points 



47. The component of the numerical model involving interior points of 



each channel is obtained by replacing the partial derivatives in Equations 7 



and 8 with finite-difference representations. Using a nonuniform rectangular 



grid on the y - t plane, as shown in Figure 4, distances along a channel are 



represented by abscissas, and times are represented by ordinates. Values of a 



function a and its derivatives at a point M(i + 1/2, J + 8 At) can be written 



as 



1 (9) 



a(AO= -i [a(i + l.j + 1)+ a(i,j + 1)16 + -i [a(i + l,j)+ a(i,j)] (1 - 6) 



2 a 



.3a(W)_ ^ l{[a(i + i,j + 1) + a{i,j + 1)] - (a(i + l,j) + a(i,j)]}-^ 



20 



