Modelling the advection equation under water hammer conditions

The quality of water delivered by a distribution network may degrade for many reasons. This research considers one of these, focusing attention on the connection between water quality and the hydraulic events in a pipe system. More specifically, pressure and velocity variations associated with hydraulic transients or water hammer conditions, particularly through leaks and rapid device adjustments, have the potential to degrade water quality. In most previous applications, numerical transport schemes have been coupled to quasi-steady hydraulic models. By contrast, the current contribution couples a finite difference solution of the advection-reaction equation to a fully unsteady, method of characteristics (MOC) based, hydraulic solution. Depending on system properties, the effects of advection, compressibility and reaction may be evident in the modelled response. The numerical properties of consistency, stability and convergence of the proposed model are investigated both analytically and numerically. Although some case studies have revealed important water quality implications associated with dynamic conditions, particularly in cases of contaminated water intrusion, it should be admitted that many transient simulations exhibit few differences compared with quasi-steady results.