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Published in:
2016 | Supplement | Chapter
From River Rhine Alarm Model to Water Supply Network Simulation by the Method of Lines
Author : Gerd Steinebach
Published in: Progress in Industrial Mathematics at ECMI 2014
Publisher: Springer International Publishing
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Abstract
In this paper an overview on modelling techniques and numerical methods applied to problems in water network simulation is given. The considered applications cover river alarm systems (Rentrop and Steinebach, Surv Math Ind 6:245–265, 1997), water level forecast methods (Steinebach and Wilke, J CIWEM 14(1):39–44, 2000) up to sewer and water supply networks (Steinebach et al., Mathematical Optimization of Water Networks Martin. Springer, Basel, 2012).
The hyperbolic modelling equations are derived from mass and momentum conservation laws. A typical example are the well known Saint-Venant equations. For their numerical solution a conservative semi-discretisation in space by finite differences is proposed. A new well-balanced space discretisation scheme is presented which improves the local Lax-Friedrichs approach applied so far. Higher order discretisations are achieved by WENO methods (Kurganov and Levy, SIAM J Sci Comput 22(4):1461–1488, 2000).
Together with appropriate boundary and coupling conditions this method of lines approach leads to an index-one DAE system. Efficient solution of the DAE system is the topic of Jax and Steinebach (ROW methods adapted to network simulation for fluid flow, in preparation).