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Adjoint-based error control for the simulation and optimization of gas and water supply networks

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  • Domschke, Pia
  • Kolb, Oliver
  • Lang, Jens

Abstract

In this work, the simulation and optimization of transport processes through gas and water supply networks is considered. Those networks mainly consist of pipes as well as other components like valves, tanks and compressor/pumping stations. These components are modeled via algebraic equations or ODEs while the flow of gas/water through pipelines is described by a hierarchy of models starting from a hyperbolic system of PDEs down to algebraic equations. We present a consistent modeling of the network and derive adjoint equations for the whole system including initial, coupling and boundary conditions. These equations are suitable to compute gradients for optimization tasks but can also be used to estimate the accuracy of models and the discretization with respect to a given cost functional. With these error estimators we present an algorithm that automatically steers the discretization and the models used to maintain a given accuracy. We show numerical experiments for the simulation algorithm as well as the applicability in an optimization framework.

Suggested Citation

  • Domschke, Pia & Kolb, Oliver & Lang, Jens, 2015. "Adjoint-based error control for the simulation and optimization of gas and water supply networks," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 1003-1018.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:1003-1018
    DOI: 10.1016/j.amc.2015.03.029
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    References listed on IDEAS

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    1. P. Spellucci, 1998. "A new technique for inconsistent QP problems in the SQP method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(3), pages 355-400, October.
    2. Pia Domschke & Bjorn Geißler & Oliver Kolb & Jens Lang & Alexander Martin & Antonio Morsi, 2011. "Combination of Nonlinear and Linear Optimization of Transient Gas Networks," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 605-617, November.
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    Cited by:

    1. Naumann, Alexander & Kolb, Oliver & Semplice, Matteo, 2018. "On a third order CWENO boundary treatment with application to networks of hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 252-270.
    2. Pia Domschke & Oliver Kolb & Jens Lang, 2022. "Fast and reliable transient simulation and continuous optimization of large-scale gas networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 475-501, June.
    3. Terrence W. K. Mak & Pascal Van Hentenryck & Anatoly Zlotnik & Russell Bent, 2019. "Dynamic Compressor Optimization in Natural Gas Pipeline Systems," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 40-65, February.
    4. Borsche, Raul & Eimer, Matthias & Siedow, Norbert, 2019. "A local time stepping method for thermal energy transport in district heating networks," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 215-229.

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