Topological Index Criteria in DAE for Water Networks

Please always quote using this URN: urn:nbn:de:0297-zib-8821
  • 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.

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Author:Marc Steinbach
Document Type:ZIB-Report
Tag:Water network; differential-algebraic equation; solvability; topological index criteria
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems
94-XX INFORMATION AND COMMUNICATION, CIRCUITS / 94Cxx Circuits, networks / 94C15 Applications of graph theory [See also 05Cxx, 68R10]
Date of first Publication:2005/11/29
Series (Serial Number):ZIB-Report (05-49)