Graph-Theoretical Formulation for Channel Network Flows - MATLAB Code and Data

Full description

Gradually varied and unsteady flow frequently occurs in various open channel networks, including irrigation systems, canal networks, stormwater networks and sewer systems. While different simulation methods have been developed, it is changeling to maintain computational efficiency while preserving the accuracy, leading to obstacles for online real-time applications. This paper presents a novel method to formulate this problem using graph theory and an electrical equivalent scheme. The governing equations for all nodes and channel sections, expressed in electrical-circuit form, are elegantly integrated using matrices and vectors representing characteristics and topology of the network. A compact formulation comprising just two matrix equations is obtained to represent the flow in an open channel network of arbitrary configuration. Compared with traditional methods, this new approach can achieve high efficiency while retaining high fidelity, and it provides a generalised framework for modelling any configuration without the need to separately list governing equations for each node and channel. Validation of the proposed method is demonstrated by comparing results from different channel networks with those obtained using traditional approaches.