Application of Relaxation Scheme to Wave-Propagation Simulation in Open-Channel Networks

This paper presents the application of a nonoscillatory second order relaxation scheme to simulation of flow in open channel networks. The approach is based on the Saint Venant equations written in conservative form. Junction flow conditions in the channel network are solved explicitly using the continuity principle at each junction and the characteristic equations. When compared with other models and algorithms, which are based on the Saint Venant equation in either nonconservative or conservative form, the proposed algorithm is of higher accuracy and is applicable to cases where propagation of a shock wave or discontinuity is involved. In this paper we discuss the application of the proposed algorithm to both single channel and channel network problems, both with and without shock waves. Numerical results obtained are presented comparatively with analytical solutions or results obtained from other numerical solutions wherever applicable.