Structure-preserving discretization of a coupled Allen-Cahn and heat equation system

Authors

Antoine Bendimerad-Hohl, Ghislain Haine, Denis Matignon, Bernhard Maschke

Abstract

Eutectic freeze crystallisation is a promising way of purifying water for it may require less energy than other methods. In order to simulate such a process, phase field models such as Allen-Cahn and Cahn-Hilliard can be used. In this paper, a port-Hamiltonian formulation of the Allen-Cahn equations is used and coupled to heat conduction, which allows for a thermodynamically consistent system to be written with the help of the entropy functional. In a second part, the Partitioned Finite Element Method, a structure-preserving spatial discretization method, is applied to the Allen-Cahn equation; it gives rise to an exact free energy balance at the discrete level. Finally some numerical results are presented.

Keywords

port-Hamiltonian systems; Partitioned Finite Element Method; Phase Field; Diffuse Interface; Solidification process; Entropy

Citation

• Journal: IFAC-PapersOnLine
• Year: 2022
• Volume: 55
• Issue: 18
• Pages: 99–104
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2022.08.037
• Note: 4th IFAC Workshop on Thermodynamics Foundations of Mathematical Systems Theory TFMST 2022- Montreal, Canada, 25–27 July 2022

BibTeX

@article{Bendimerad_Hohl_2022,
  title={{Structure-preserving discretization of a coupled Allen-Cahn and heat equation system}},
  volume={55},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2022.08.037},
  number={18},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Bendimerad-Hohl, Antoine and Haine, Ghislain and Matignon, Denis and Maschke, Bernhard},
  year={2022},
  pages={99--104}
}

Download the bib file

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