Structure‐preserving discretization of a port‐Hamiltonian formulation of the non‐isothermal Euler equations
Authors
Sarah-Alexa Hauschild, Nicole Marheineke
Abstract
The port‐Hamiltonian (pH) formulation of partial‐differential equations (pdes) and their numerical treatment have been elaborately studied lately. In this context we consider the non‐isothermal flow of a compressible fluid. Starting from the pdes we derive a pH formulation for Euler‐type equations in the weak sense on one pipe. One advantage of pH systems is that fundamental physical properties, like energy dissipation and mass conservation, are encoded in the system structure. Therefore, structure‐preservation during approximation is most important. Based on the weak form we introduce a structure‐preserving Galerkin approximation with mixed finite elements. A numerical example supports the theoretical results.
Citation
- Journal: PAMM
- Year: 2021
- Volume: 20
- Issue: 1
- Pages:
- Publisher: Wiley
- DOI: 10.1002/pamm.202000014
BibTeX
@article{Hauschild_2021,
title={{Structure‐preserving discretization of a port‐Hamiltonian formulation of the non‐isothermal Euler equations}},
volume={20},
ISSN={1617-7061},
DOI={10.1002/pamm.202000014},
number={1},
journal={PAMM},
publisher={Wiley},
author={Hauschild, Sarah-Alexa and Marheineke, Nicole},
year={2021}
}
References
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- Egger, H., Kugler, T., Liljegren-Sailer, B., Marheineke, N. & Mehrmann, V. On Structure-Preserving Model Reduction for Damped Wave Propagation in Transport Networks. SIAM J. Sci. Comput. 40, A331–A365 (2018) – 10.1137/17m1125303