A finite volume model for maintaining stationarity and reducing spurious oscillations in simulations of sewer system filling and emptying

This paper introduces a model for simulating the unsteady dynamics of sewer systems filling and emptying, offering greater accuracy and stability. This article presents two novel contributions: first, the HLLS scheme (Harten–Lax–van Leer + Source term) is adapted to ensure the preservation of stationary conditions not only in free surface flows, as originally conceived, but also in pressurized flows and mixed flow scenarios. Second, a new method is proposed for the treatment of open channel flow cells near pressurization or adjacent to pressurized cells to minimize spurious oscillations when utilizing the two-component pressure approach (TPA) model. To verify the new model's effectiveness, it was tested for various conditions against the outcomes of the Open Source Field Operation and Manipulation (OpenFOAM) computational fluid dynamics (CFD) model. Furthermore, to demonstrate the model's potential for simulating real systems, the model was applied to three sewer systems that closely resemble real-world conditions, each of which had been intentionally modified for confidentiality purposes. The results show that the improved model successfully maintains stationary conditions within a sloped pipe across various flow conditions, while also preventing spurious oscillations at mixed flow interfaces even when using a pressure wave speed of 1000 m s−1.