TY - GEN A1 - Steinbach, Marc T1 - Topological Index Criteria in DAE for Water Networks N2 - The dynamics of pressurized water distribution networks are naturally modeled by differential algebraic equations (DAE). This paper investigates fundamental structural properties of such a DAE model under weak regularity assumptions. The usual partial derivative-based index-1 condition is shown to be necessary and sufficient for several index concepts, as well as sufficient for solvability in a strong sense. Using the physical properties of nonlinear network elements and the inherent saddle point structure of network hydraulics, we then derive purely topological index criteria based on the network graph and the choice of control variables. Several examples illustrate the theoretical results and explore different non-index-1 situations. A brief discussion of the implications for operative planning by discrete time DAE boundary value problems concludes the paper. T3 - ZIB-Report - 05-49 KW - Water network KW - differential-algebraic equation KW - solvability KW - topological index criteria Y1 - 2005 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/882 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-8821 ER -