An algorithm is presented for computing the water surface profiles in
steady-state gradually varied Bows in tree-type open-channel networks.
The algorithm is based on the principles of (1) decomposing the chann
el network into units that are as small as possible; (2) solving the s
maller units using an appropriate method, such as the fourth-order Run
ge-Kutta method; and (3) connecting the solutions for the smaller unit
s to obtain the final solution for the whole network using the Shootin
g Method. Elementary graph theoretical concepts are utilized to choose
the iterative how variables so that the small units can be solved eff
iciently. The algorithm is computationally more efficient than the dir
ect method using the Newton-Raphson technique by an order of magnitude
. It does not involve the solution of large matrix equations. The effi
ciency of the algorithm is illustrated by solving an example tree-type
channel network with 42 nodes, 41 channels, and a total of 429 grid p
oints. The proposed method will also be very useful in the design and
optimization of tree-type channel networks.