Model Reduction for a Port-Hamiltonian Formulation of the Euler Equations

Authors

Sarah-Alexa Hauschild, Nicole Marheineke

Abstract

The port-Hamiltonian (pH) formulation of partial-differential equations and their numerical treatment have been elaborately studied lately. This energy-based formulation encodes physical principles in the system structure and the pH-character is inherited during coupling. Considering a non-isothermal compressible fluid flow in a pipe, we propose a pH-model on PDE-level, which is advantageous for structure-preserving approximations. Based on Galerkin projection with compatible finite dimensional spaces we preserve the pH-structure during space discretization and model reduction. Numerical results support our theoretical findings.

Citation

• ISBN: 9783031118173
• Publisher: Springer International Publishing
• DOI: 10.1007/978-3-031-11818-0_1
• Note: European Consortium for Mathematics in Industry

BibTeX

@inbook{Hauschild_2022,
  title={{Model Reduction for a Port-Hamiltonian Formulation of the Euler Equations}},
  ISBN={9783031118180},
  ISSN={2198-3283},
  DOI={10.1007/978-3-031-11818-0_1},
  booktitle={{Progress in Industrial Mathematics at ECMI 2021}},
  publisher={Springer International Publishing},
  author={Hauschild, Sarah-Alexa and Marheineke, Nicole},
  year={2022},
  pages={1--7}
}

Download the bib file

References

• H. Egger. A mixed variational discretization for non-isothermal compressible flow in pipelines. arXiv:1611.03368, 2016.
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• Hauschild, S.-A. & Marheineke, N. Structure‐preserving discretization of a port‐Hamiltonian formulation of the non‐isothermal Euler equations. PAMM vol. 20 (2021) – 10.1002/pamm.202000014
• Liljegren-Sailer, B. & Marheineke, N. On Port-Hamiltonian Approximation of a Nonlinear Flow Problem on Networks. SIAM Journal on Scientific Computing vol. 44 B834–B859 (2022) – 10.1137/21m1443480
• Mehrmann, V. & Morandin, R. Structure-preserving discretization for port-Hamiltonian descriptor systems. 2019 IEEE 58th Conference on Decision and Control (CDC) 6863–6868 (2019) doi:10.1109/cdc40024.2019.9030180 – 10.1109/cdc40024.2019.9030180