GVF computation in tree-type channel networks

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