A graph-based frequency-domain model enables highly efficient modelling of sewer network hydraulics

Hydraulic modeling is essential for sewer network management; however, the high computational demand of traditional time-domain solvers often limits their utility in iterative diagnostic applications. This study introduces a Graph-based Frequency-domain Model (GFM) to overcome this bottleneck. By leveraging graph theory and the Laplace transform, GFM decouples the spatial and temporal dependencies of the network, converting complex differential equations into efficient matrix operations. The model exploits a key finding: in our study, sewer systems behave as low-pass filters, where 99.9% of spectral energy is concentrated in the lowest 1% frequencies. This property allows GFM to reconstruct transient responses at arbitrary nodes with high accuracy while circumventing numerical stability constraints, maintaining a relative L₂ error below 2% for surge peaks up to 2.6 times the baseline flow. Validated on a real-world trunk sewer and the large-scale complete network, GFM achieves two to three orders of magnitude speedup over standard time-domain solvers, providing a scalable framework for real-time hydraulic diagnosis.