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Hybrid Numerical Scheme of Preissmann Slot Model for Transient Mixed Flows

The Preissmann slot model is one of the most widely used models to conceptualize both free-surface and pressurized flows in urban drainage systems. Despite its simplicity and wide range of applications, numerical solutions of the Preissmann slot model suffer from the spurious oscillations, especially when flow conditions switch from free-surface flow to pressurized flow. To overcome this problem, a new hybrid numerical flux solver of the Preissmann slot model is proposed herein, in which the upwind flux solver is combined with the centered flux solver. Numerical experiments are conducted for multiple flow conditions such as typical filling, pipe-filling, and transition-flow conditions. The numerical results indicate that the proposed scheme generally outperforms the conventional flux schemes for various hydraulic conditions and wave velocities. The proposed scheme should be useful to further enhance integrated urban water modeling in which transient mixed flow conditions significantly impact the simulation accuracy during extreme floods.