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Index-Preserving Model Order Reduction for Differential-Algebraic Systems Arising in Gas Transport Networks

  • Nicodemus BanagaayaEmail author
  • Peter Benner
  • Sara Grundel
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)

Abstract

Gas transportation networks can be modeled by the isothermal Euler equations. Spatial discretization of these equations leads to large-scale systems of nonlinear differential-algebraic equations. Often, model order reduction is necessary for simulation of the discretized network equations under time constraints during operation. Direct reduction of such systems leads to ordinary differential equations which are very difficult to simulate especially if the index of the differential-algebraic equation is greater than one. We consider gas flow through a gas transportation network with more than one supply node which leads to differential-algebraic equations of index 2. We propose an index-aware approach which first automatically decouples the index 2 gas network into differential and algebraic parts leading to reduced-order models which are also differential-algebraic equations of the same index. This approach gives very accurate reduced order models which can be simulated using any standard ordinary differential equation numerical solver leading to accurate solutions.

Notes

Acknowledgements

This work was supported by the German Federal Ministry for Economic Affairs and Energy, in the joint project: “MathEnergy—Mathematical Key Technologies for Evolving Energy Grids”, sub-project: Model Order Reduction (Grant number: 0324019B).

References

  1. 1.
    Banagaaya, N.: Index-aware model order reduction methods. Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, Netherlands (2014)Google Scholar
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    Banagaaya, N., Grundel, S., Benner, P.: Index-aware MOR for Gas Transport Networks. In: Proccedings of IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, May 22–25, 2018, pp. 191–207. Springer, Cham (2020)Google Scholar
  3. 3.
    Grundel, S., Jansen, L., Hornung, N., Clees, T., Tischendorf, C., Benner, P.: Model order reduction of differential algebraic equations arising from the simulation of gas transport networks. In: Schöps, S., Bartel, A., Günther, M., ter Maten, W.J.W., Müller, P.C. (eds.) Progress in Differential-Algebraic Equations, pp. 183–205. Springer, Berlin (2014)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Nicodemus Banagaaya
    • 1
    Email author
  • Peter Benner
    • 1
  • Sara Grundel
    • 1
  1. 1.Max Planck Institute for Dynamics of Complex Technical SystemsMagdeburgGermany

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