Simple, Robust, and Efficient Algorithm for Gradually Varied Subcritical Flow Simulation in General Channel Networks

Abstract

This paper details the development of a method for subcritical flow modeling in channel networks by using the implicit finite-difference method. The method treats backwater effects at the junction points on the basis of junction-point water stage prediction and correction (JPWSPC). It is applicable to flows in both looped and nonlooped channel networks and has no requirement on the flow directions. The method is implemented in a numerical model, in which the Saint-Venant equations are discretized by using the four-point implicit Preissmann scheme, and the resulting nonlinear system of equations is solved by using the Newton-Raphson method. With the help of JPWSPC, each branch is computed independently. This guarantees the simplicity, efficiency, and robustness of the numerical model. The model is applied to two hypothetic channel networks and a real-life river network in South China. All the networks contain both branched and looped structures. The simulated results compare well with the results from literature or the measurements.