Importance of numerical efficiency for real time control of transient gravity flows in sewers

Numerical efficiency-achieving a given level of accuracy with the least Central Processing Unit (CPU) time-is of paramount importance in transient flow modeling of sewerage systems. This is particularly important (i) for large sewerage systems containing a wide range of flow controls such as gates and pumps and/or (ii) for systems requiring real-time flow model for their operation. The Tunnel and Reservoir Plan (TARP), which was adopted by the Metropolitan Water Reclamation District of Greater Chicago in 1972 to address the combined sewer overflow (CSO) pollution and flooding problems in the Chicago-land area, is an example of systems requiring a highly efficient transient model. In this paper, the accuracy and efficiency of two second-order explicit Finite-Volume Godunov-Type Schemes (GTS) and one fixed-grid Method of Characteristics (MOC) scheme with space-line interpolation are investigated using problems whose solution contain features that are relevant to transient flows in sewers such as shocks and expansion waves. The results show that the two GTS schemes are significantly faster to execute than the MOC scheme, and in some cases, the accuracy produced by the two GTS schemes can not 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.