Performance Quantitative Assessment of Linear and Discrete Time Approximants for Dynamic Water Distribution Network Models

Water distribution networks (WDNs) exhibit nonlinear hydraulic dynamics due to pipe friction, fluid inertia, and water compressibility. This paper evaluates the accuracy of linear and discrete time approximants of a benchmark nonlinear WDN, modelled using the Elastic Water Column (EWC) approach. For this benchmark, three types of approximants are used: a linear continuous-time model, a nonlinear discrete-time model, and a linear discrete-time model. These approximants are compared with the original nonlinear continuous-time model, using the following criteria: the Integral Absolute Error (IAE), the Integral Square Error (ISE), the Integral Time Absolute Error (ITAE), the Integral Time Square Error (ITSE), and the Infinity Norm Error (INE).