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A Unified (P)DAE Modeling Approach for Flow Networks

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Progress in Differential-Algebraic Equations

Part of the book series: Differential-Algebraic Equations Forum ((DAEF))

Abstract

We present a unified modeling approach for different types of flow networks, for instance electric circuits, water and gas supplying networks. In all cases the flow network is described by the pressures at the nodes of the network and the flows through the branches of the network. It is shown that the mass balance equations at each node are independent of the type of flow medium and can be described by the use of incidence matrices reflecting the network topology. Additionally, various types of net element models are presented. Finally, all network describing equations are summarized for some prototype networks which differ by the various net element models. They yield in pure linear/nonlinear equation systems, differential-algebraic systems or partial differential equation systems. All of them may have serious rank changes in the model functions if switching elements belong to the network. The model descriptions presented here keep all the network structure information and can be exploited for the analysis, numerical simulation and optimization of such networks.

Mathematics Subject Classification (2010) 93A30 ⋅ 34A09 ⋅ 35M20 ⋅ 94C05 ⋅ 34B45 ⋅ 76N15

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Authors and Affiliations

  1. Humboldt-Univerität zu Berlin, 10099, Berlin, Germany

    Lennart Jansen & Caren Tischendorf

Authors
  1. Lennart Jansen
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  2. Caren Tischendorf
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Correspondence to Caren Tischendorf .

Editor information

Editors and Affiliations

  1. Technische Universität Darmstadt, Graduate School CE, Darmstadt, Germany

    Sebastian Schöps

  2. Bergische Universität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany

    Andreas Bartel

  3. Bergische Univeirsität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany

    Michael Günther

  4. Eindhoven University of Technology, Dept. Mathematics & Comp. Sci., Eindhoven, The Netherlands

    E. Jan W. ter Maten

  5. Bergische Universität Wuppertal, Dept. Safety Control Engineering, Wuppertal, Germany

    Peter C Müller

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Jansen, L., Tischendorf, C. (2014). A Unified (P)DAE Modeling Approach for Flow Networks. In: Schöps, S., Bartel, A., Günther, M., ter Maten, E., Müller, P. (eds) Progress in Differential-Algebraic Equations. Differential-Algebraic Equations Forum. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44926-4_7

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