Comparison of Gradually Varied Flow Computation Algorithms for Open-Channel Network

Abstract

This paper presents a comparison of two algorithms—the forward-elimination and branch-segment transformation equations— for separating out end-node variables for each branch to model both steady and unsteady flows in branched and looped canal networks. In addition, the performance of the recursive forward-elimination method is compared with the standard forward-elimination method. The Saint-Venant equations are discretized using the four-point implicit Preissmann scheme, and the resulting nonlinear system of equations is solved using the Newton-Raphson method. The algorithm using branch-segment transformation equations is found to be at least five times faster than the algorithm using the forward-elimination method. Further, the algorithm using branch-segment transformation equations requires less computer storage than the algorithm using the forward-elimination method, particularly when only nonzero elements of the global matrix are stored. Comparison between the Gauss-elimination method and the sparse matrix solution technique for the solution of the global matrix revealed that the sparse matrix solution technique takes less computational time than the Gauss- elimination method.