Graph-Theoretical Formulation of Gradually Varied Flow in Open Channel Networks - MATLAB Code

Gradually varied flow frequently occurs in various open channel networks, including irrigation systems, canal networks, river systems, stormwater networks, and sewer systems. This paper presents a novel method to formulate this problem using graph theory. The characteristics and topology of an arbitrary channel network can first be defined using matrix and vector formats. The governing equations for all nodes and channel sections are then elegantly integrated using these matrices and vectors. A compact formulation comprising just two matrix equations is obtained to represent the gradually varied flow in an open channel network. Compared with traditional methods, this new approach eliminates the need to list separate equations for different types of nodes and to sequentially formulate equations for each channel. As a result, it provides a generalized process for modelling any channel network. The method also treats internal nodes as inflow/outflow boundaries, enabling more flexible applications—such as modelling complex drainage systems with manholes receiving runoff. Validation of the proposed method is demonstrated by comparing results from various channel networks with those obtained using traditional approaches.