Godunov-type solutions for transient flows in sewers

This work is part of a long term project which aims at developing a hydraulic model for real-time simulation of unsteady flows in sewers ranging from gravity flows, to partly gravity-partly surcharged flows to fully surcharged flows. The success of this project hinges on the ability of the hydraulic model to handle a wide range of complex boundaries and to provide accurate solutions with the least central processing unit time. This first paper focuses on the development and assessment of two second-order explicit finite-volume Godunov-type schemes (GTS) for unsteady gravity flows in sewers, but with no surcharging. Traditionally, hydraulic transients have been modeled using the method of characteristics (MOC), which is noted for its ability to handle complex boundary conditions (BCs). The two GTS described herein incorporate BCs in a similar manner to the MOC. The accuracy and efficiency of these GTS schemes are investigated using problems whose solution contains features that are relevant to transient flows in sewers such as shock, expansion, and roll waves. The results show that these GTS schemes are significantly faster to execute than the fixed-grid MOC scheme with space-line interpolation, and in some cases, the accuracy produced by the two GTS schemes cannot be matched by the accuracy of the MOC scheme, even when a Courant number close to one and a large number of grids is used. Furthermore, unlike the MOC solutions, which exhibit increasing numerical dissipation with decreasing Courant numbers, the resolution of the shock fronts was maintained by the GTS schemes even for very low Courant numbers (0.001).