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

Bendimerad-Hohl, Antoine and Haine, Ghislain and Matignon, Denis and Maschke, Bernhard Structure-preserving discretization of a coupled Allen-Cahn and heat equation system. (2022) In: 4th IFAC Workshop on Thermodynamic Foundations of Mathematical Systems Theory - TFMST 2022, 25 July 2022 - 27 July 2022 (Montreal, Canada).

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Official URL: https://doi.org/10.1016/j.ifacol.2022.08.037


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.

Item Type:Conference or Workshop Item (Paper)
Additional Information:This is an open access article under the CC BY-NC-ND license. Vol. 55 n° 18.
HAL Id:hal-03887977
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Supérieure de Chimie Physique et Electronique de Lyon (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Université de Lyon - UDL (FRANCE)
Laboratory name:
Deposited On:07 Dec 2022 09:17

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