A Topology Based Discretization of PDAEs Describing Water Transportation Networks.

We consider partial differential algebraic systems (PDAEs) describing water transportation networks. Similar to the approach in [6], we follow the method of lines for the discretization. However, we do not consider free surface flow models but pressure flow models covering hydraulic shocks. Moreover, we include switching models reflecting the on/off state of pumpes and valves. Aiming at a stable numerical simulation of the PDAEs we present a topology based spatial discretization that results in a differential algebraic system (DAE) of index 1. Furthermore we show that the DAE index can be higher than 1 if the spatial discretization is not adapted to the position of reservoirs and demand nodes within the network. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]