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Model and Discretization Error Adaptivity Within Stationary Gas Transport Optimization

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Abstract

The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to highly simplified algebraic equations, modeling and discretization error estimates are presented to control the overall error in an optimization method for stationary and isothermal gas flows. The error control is realized by switching to more detailed models or finer discretizations if necessary to guarantee that a prescribed model and discretization error tolerance is satisfied in the end. We prove convergence of the adaptively controlled optimization method and illustrate the new approach with numerical examples.

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  1. http://www.mso.math.fau.de/edom/projects/lamatto.html

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Acknowledgements

This research has been performed as part of the Energie Campus Nürnberg and is supported by funding of the Bavarian State Government. The authors acknowledge funding through the DFG Transregio TRR 154, subprojects A05, B03, and B08.

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Authors and Affiliations

  1. Institut für Mathematik, MA 4-5, TU Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Volker Mehrmann & Jeroen J. Stolwijk

  2. Friedrich-Alexander-Universität Erlangen-Nürnberg, Discrete Optimization, Cauerstr. 11, 91058, Erlangen, Germany

    Martin Schmidt

  3. Energie Campus Nürnberg, Fürther Str. 250, 90429, Nürnberg, Germany

    Martin Schmidt

Authors
  1. Volker Mehrmann
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  3. Jeroen J. Stolwijk
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Correspondence to Volker Mehrmann.

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Dedicated to Hans Georg Bock on the occasion of his 70th birthday.

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Mehrmann, V., Schmidt, M. & Stolwijk, J.J. Model and Discretization Error Adaptivity Within Stationary Gas Transport Optimization. Vietnam J. Math. 46, 779–801 (2018). https://doi.org/10.1007/s10013-018-0303-1

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