Numerical study on accuracy of frequency-domain modelling of transients

Modelling pressure transients within pipeline systems has acquired considerable importance in the last decades, since it allows for the analysis of the pressure surge behaviour in the system (Brunone et al., 2014; Lee, Duan, Ghidaoui, & Karney, 2013; Zecchin, Simpson, Lambert, White, & Vítkovský, 2009) and the detection of anomalies, e.g. leaks (Brunone, 1999; Capponi, Ferrante, Zecchin, & Gong, 2017; Duan, Lee, Ghidaoui, & Tung, 2010; Ferrante, Brunone, & Meniconi, 2009; Ferrante, Brunone, Meniconi, Capponi, & Massari, 2014; Ferrante et al., 2016; Gong, Lambert, Simpson, & Zecchin, 2013; Gong, Zecchin, Simpson, & Lambert, 2014; Meniconi et al., 2015; Zecchin, Lambert, Simpson, & White, 2010), partial blockages (Lee, Vítkovský, Lambert, Simpson, & Liggett, 2008; Meniconi, Brunone, Ferrante, & Massari, 2012; Meniconi et al., 2013), illegal branches (Meniconi, Brunone, Ferrante, & Massari, 2011), and pipe wall deterioration (Gong et al., 2015, 2016; Stephens, Lambert, & Simpson, 2013). When a hydraulic transient event is simulated, the governing equations (Chaudhry, 2014; Wylie & Streeter, 1993) can be solved in the time domain (e.g. with the method of characteristics, MOC), or, after being linearized, in the frequency domain. The main approaches used to model transients in the frequency domain for simple systems are the impedance method (IM) (Wylie, 1965) and the transfer matrix method (Chaudhry, 1970), while the impedance matrix method (Kim, 2007) and the admittance matrix method (Zecchin et al., 2010) are used to model more complex systems. Frequency-domain models can produce time-domain simulations by an inverse transform process, such as the inverse-Fourier transform (Chaudhry, 1970; Ferrante & Brunone, 2003; Suo & Wylie, 1989), or the inverse Laplace transform (Zecchin, Lambert, & Simpson, 2012). For a relatively simple system, time-domain modelling, by means of the MOC, is reasonably accurate and provides a robust solution within a reasonable computational time, taking into account nonlinearities such as friction. However, this model requires a fixed time-space grid that often implies approximations in the simulation of a transient, and, when the system becomes more complex, it takes a significant time for computation. The frequency-domain models do not need a timespace grid so they can simulate precisely the arrival times of the reflected waves at a chosen measurement section (Covas, Ramos, & Almeida, 2005; Suo & Wylie, 1989). The solution of the Fourier transform of the linearized governing equations can be then evaluated in the time-domain, so that these models map the system behaviour from frequency to time and continuously in space. Moreover frequency-domain models take less