Stability and asymptotic analysis for instationary gas transport via relative energy estimates

Authors

H. Egger, J. Giesselmann

Abstract

We consider the transport of gas in long pipes and pipeline networks for which the dynamics are dominated by friction at the pipe walls. The governing equations can be formulated as an abstract dissipative Hamiltonian system which allows us to derive perturbation bounds via relative energy estimates using a problem adapted nonlinear analysis. As particular consequences of these results, we are able to prove stability estimates with respect to initial conditions and model parameters and we conduct a quantitative asymptotic analysis in the high friction limit. Our results are established first for the flow in a single pipe and we then extend our analysis to pipe networks in the spirit of energy-based port-Hamiltonian modelling.

Keywords

35B25; 35B35; 35B40; 35L65

Citation

• Journal: Numerische Mathematik
• Year: 2023
• Volume: 153
• Issue: 4
• Pages: 701–728
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00211-023-01349-9

BibTeX

@article{Egger_2023,
  title={{Stability and asymptotic analysis for instationary gas transport via relative energy estimates}},
  volume={153},
  ISSN={0945-3245},
  DOI={10.1007/s00211-023-01349-9},
  number={4},
  journal={Numerische Mathematik},
  publisher={Springer Science and Business Media LLC},
  author={Egger, H. and Giesselmann, J.},
  year={2023},
  pages={701--728}
}

Download the bib file

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