Well-balanced finite volume model for transient mixed flow in sewer pipe network Open Access

Numerical simulation of free-surface and pressurized mixed flow in urban sewer networks is important for the protection of urban areas. The numerical model needs to accurately represent the flow regime transitions and maintain horizontal still water conditions when the sewer network is closed (i.e., the well-balanced property). This paper presents a well-balanced finite volume model for sewer networks based on the HLLS (Harten–Lax–van Leer + Source term) solver. A novel boundary solver is proposed, which directly incorporates the source term to maintain stationary flow conditions and efficiently manages transitions between various flow regimes at interfaces between pipes and junctions. In addition, the update procedure for pipes and junctions to guarantee mass conservation and solution stability is illustrated. The numerical model is tested in various scenarios to validate its accuracy and stability. The results demonstrate that the model can accurately predict the sewer network filling and emptying while maintaining the well-balanced property.

• The augmented HLLS solver is implemented in the sewer pipe model to maintain the lake-at-rest condition.

• A novel boundary solver is proposed to handle various flow regime transitions at the interfaces between pipes and junctions while ensuring the well-balanced property.

• An update procedure for pipes and junctions that guarantees mass conservation and solution stability.