Efficient Algorithm for Gradually Varied Flows in Channel Networks

This paper presents an efficient solution technique for one-dimensional unsteady flow routing through a general channel network system—dendritic, looped, divergent, or any combination of such networks. The finite difference method is used to solve the de St. Venant equations in all the branches of the network simultaneously. The number of equations to be solved at a time during any iteration is reduced to only four times the number of branches of the network. This results in a significant reduction in storage requirements and solution time. Importantly, the algorithm does not require any special node numbering schemes and the nodes can be numbered independently for each branch. The algorithm is also suitable for programming on a parallel-processing computer.