A novel relaxed modified pipe hydrodynamic model for mixed flow simulation

In this study, we propose a novel modified pipe hydrodynamic model with a partial relaxation approach and develop a corresponding numerical algorithm within the framework of the finite volume method for its computation to enable robust, accurate, and comprehensive pipe modeling. The proposed numerical model provides some key improvements compared to existing numerical schemes for simulating mixed pipe flows: (1) it is capable of preserving both moving- and stationary-water steady states, and (2) it effectively reduces post-bore oscillations while maintaining second-order accuracy in the non-pressurized regime for unsteady pipe flows. Such improvements have been verified against theoretical and experimental data through tests involving both smooth and sharp-gradient steady and unsteady flows across various regimes in straight and locally bent circular pipes, which are fundamental elements of stormwater drainage, sewage networks, and industrial process pipelines. The proposed pipe flow model can be further improved regarding post-pore stability by utilizing specific post-bore oscillation suppression techniques, and it can be integrated into a practical hydraulic modeling tool for pipeline networks in future work.