Hierarchical Modelling and Model Adaptivity for Gas Flow on Networks

  • Pia Bales
  • Oliver Kolb
  • Jens Lang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5544)


We are interested in the simulation and optimization of gas transport in networks. Different regions of the network may be modelled by different equations. There are three models based on the Euler equations that describe the gas flow in pipelines qualitatively different: a nonlinear model, a semilinear model and a stationary also called algebraic model. For the whole network, adequate initial and boundary values as well as coupling conditions at the junctions are needed. Using adjoint techniques, one can specify model error estimators for the simplified models. A strategy to adaptively apply the different models in different regions of the network while maintaining the accuracy of the solution is presented.


model adaptivity adjoint equations gas flow 


  1. 1.
    Bales, P.: Hierarchische Modellierung der Eulerschen Flussgleichungen in der Gasdynamik. Diploma thesis, TU Darmstadt (2005)Google Scholar
  2. 2.
    Bales, P., Geißler, B., Kolb, O., Lang, J., Martin, A., Morsi, A.: Comparison of Linear and Nonlinear Optimization of Transient Gas Networks. Preprint No. 2552, TU Darmstadt (2008)Google Scholar
  3. 3.
    Banda, M., Herty, M., Klar, A.: Coupling conditions for gas networks governed by the isothermal euler equations. NHM 1(2), 295–314 (2006)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Banda, M., Herty, M., Klar, A.: Gas flow in pipeline networks. NHM 1(1), 41–56 (2006)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Becker, R., Rannacher, R.: An optimal control approach to a posteriori error estimation in finite element methods. Acta numerica 10, 1–102 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Braack, M., Ern, A.: A posteriori control of modeling errors and discretization errors. SIAM Multiscale Model. Simul. 1(2), 221–238 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kolb, O., Lang, J., Bales, P.: Adaptive linearization for the optimal control problem of gas flow in pipeline networks. Preprint No. 2553, TU Darmstadt (2008)Google Scholar
  8. 8.
    Martin, A., Möller, M., Moritz, S.: Mixed integer models for the stationary case of gas network optimization. Math. Prog. 105, 563–582 (2006)zbMATHCrossRefGoogle Scholar
  9. 9.
    Moritz, S.: A Mixed Integer Approach for the Transient Case of Gas Network Optimization. PhD thesis, TU Darmstadt (2006)Google Scholar
  10. 10.
    Sekirnjak, E.: Transiente Technische Optimierung. Concept, PSI AG (2000)Google Scholar
  11. 11.

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Pia Bales
    • 1
  • Oliver Kolb
    • 1
  • Jens Lang
    • 1
  1. 1.Technische Universität DarmstadtDarmstadtGermany

Personalised recommendations