Low dimensional modeling of Double T-junctions in water distribution networks using Kriging interpolation and Delaunay triangulation

• Published in: International journal of mathematics for industry (Online) Vol. 9; no. 1; p. 1
• Main Authors: Gilbert, Denis, Mortazavi, Iraj, Piller, Olivier, Ung, Hervé
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 20.01.2017; World Scientific Publishing Co. Pte., Ltd; Springer
• Subjects: Algorithms; Applications of Mathematics; Artificial Intelligence; Calibration; Computer Science; Design of experiments; Design techniques; Engineering Sciences; Math Applications in Computer Science; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Modeling and Simulation; Original Article; Quantitative Finance; Reynolds number; Simulation; Spectral Theory; Water quality; CFD; Turbulent; Transport modeling; Imperfect mixing; 1-D reduced model; Design of experiment; Delaunay triangulation; Kriging; Water distribution network; Laminar; water distribution system; RESEAU DE DISTRIBUTION D'EAU; PLAN D'EXPERIENCE; MODELISATION; ECOULEMENT TURBULENT; simulation; ECOULEMENT LAMINAIRE; turbulent flow; transport; modelling; contamination
• ISSN: 2198-4115; 2661-3352; 2198-4115; 2661-3344
• DOI: 10.1186/s40736-016-0026-8

Water distribution networks are subject to potential intentional contaminations to cause harm to the consumer. Reliable transport models are needed to detect, trace and follow any contaminant transported inside the network. For now, the transport of contaminants in pipes has been mostly modeled assuming perfect mixing conditions at T-junction. However, some studies have shown that it is not always the case when crosses or double T-junctions are involved. In this paper an imperfect mixing at Double T-junction model is developed considering 3-D mixing behavior. A reduced model is then constructed in the form of a 1-D law to apply it to current 1-D transport models for water distribution networks. The methodology to create such law is detailed and can be applied to any reduced model problem including multi parameters and time consuming simulations. The procedure is composed of three steps: first calibrate the Kriging interpolation method parameters; then couple it with the Delaunay triangulation method to select simulation points with maximum gain; and finally implement a 1-D law based on the simulation results and the interpolation.