Port Hamiltonian formulation of the solidification process for a pure substance: A phase field approach

Authors

Mohammed Yaghi, Françoise Couenne, Aurélie Galfré, Laurent Lefèvre, Bernhard Maschke

Abstract

In this paper we suggest a Port Hamiltonian model of the solidification process of water, using the phase field approach. Firstly, the Port Hamiltonian formulation of the dynamics of the phase field variable, governed by the Allen-Cahn equation, is recalled. It is based on adding to the phase field variable, its gradient, and extending the system with its dynamics. Secondly, the model is completed by the energy balance equation for the heat conduction and the complete Port Hamiltonian model is derived. Thirdly an Algebro-differential Port Hamiltonian representation is suggested, where the Port Hamiltonian system is defined on a Lagrangian submanifold, allowing to use directly the variables defining the thermodynamical data.

Keywords

Port Hamiltonian systems on Lagrange subspaces; Phase Field; Diffuse interface; Solidification process; Thermodynamical properties

Citation

• Journal: IFAC-PapersOnLine
• Year: 2022
• Volume: 55
• Issue: 18
• Pages: 93–98
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2022.08.036
• Note: 4th IFAC Workshop on Thermodynamics Foundations of Mathematical Systems Theory TFMST 2022- Montreal, Canada, 25–27 July 2022

BibTeX

@article{Yaghi_2022,
  title={{Port Hamiltonian formulation of the solidification process for a pure substance: A phase field approach*}},
  volume={55},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2022.08.036},
  number={18},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Yaghi, Mohammed and Couenne, Françoise and Galfré, Aurélie and Lefèvre, Laurent and Maschke, Bernhard},
  year={2022},
  pages={93--98}
}

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References

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