Unsteady flow routing in sewers using hydraulic and volumetric performance graphs

The hydraulic performance graph (HPG), which consolidates all the backwater profiles of a channel reach into a family of delivery curves, provides a summary of the momentum of flow for the entire range of conditions. Earlier research by Gonzalez-Castro (2000) demonstrated that the approximation to the momentum of flow provided by the HPG can be coupled with an implicit finite-difference solution of the continuity equation to route unsteady flows through simple, unbranched channel reaches with accuracies approaching those of dynamic wave models. The model described in this paper adds to the earlier work by introducing the volumetric performance graph (VPG), which describes the volumetric water storage in the reach for the range of flow conditions computed in the HPG. The VPG provides a summary of the conservation of mass in the reach, replacing the finite-difference solution used in the earlier work. Instead of numerically solving the Saint-Venant equations in a coupled manner, as is typically done in unsteady flow-routing, the momentum equation is solved a priori and summarized in the HPGs, which are then used to describe the momentum at each time step. The description of momentum from the HPGs is coupled with the description of continuity from the VPGs to simulate the routing in a stepwise-steady manner. Benefits of this type of modeling include: (1) computation time -the momentum equation is solved for a range of conditions and summarized, as opposed to solving at each time step, and (2) precision -momentum is solved at fine resolution, but summarized to a coarser spatial resolution.