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INTRODUCTION
Criteria for evaluating the design and operation of water distribution systems typically include cost, resilience and reliability evaluated using extended period simulations (EPSs) of system performance (e.g. Gargano & Pianese 2000; Todini 2006). Moreover, EPSs have become a common practice for real-time control of water distribution network (WDN) leakage control by simulating real-time leak losses (e.g. Almandoz et al. 2005; Giustolisi et al. 2008); finally, using EPS, the increasingly extended availability of flow and pressure sensors, including smart meters, allows for off-line as well as on-line data assimilation (Hutton et al. 2014a, 2014b; Bragalli et al. 2016) and real-time control to increase management capabilities while reducing risks of failures.
In EPS, under certain conditions (Wu & Walski 2006) such as pipe bursts (or isolation) or during excessive water demand and use, pressure at some of the nodes of a WDN may fall below the desired level, with the consequence that full demand cannot be delivered. In these cases, demand-driven approaches (DDAs) not only fail to realistically represent the actual WDN performance but also do not allow estimating such deficiencies (Laucelli et al. 2012). For this reason, when pressure falls below the desired value one needs to insert a pressure-based condition at the relevant nodes. This alternative pressure-driven approach (PDA) requires defining a flow–pressure relationship (FPR) to mathematically represent the reduced nodal flow delivered as a function of available pressure and demand.
EPANET (US EPA 2020) is a widely used, open-source software package used to model the hydraulic and water quality behavior of water distribution systems. In 2020, pressure-dependent demands were introduced in EPANET 2.2 (Rossman et al. 2020) by using a barrier function approach applied to the inverted form of the FPR, namely a pressure–flow relationship (PFR) that had already proven successful in modeling emitters. The idea originates from the way in which emitters were modeled as unconstrained pressure-dependent demands in version 2.0 of EPANET released back in 2000 (Rossman 2000) and the description on how the concept could be extended to model bounded PFRs as well (Rossman 2007).
It is well known that the direct use of the FPR often requires smoothing the curve and/or dampening of the N–R estimated changes. Elhay et al. (2016) developed in fact the energy and mass...