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

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.

To cite this paper:
Bendimerad-Hohl Antoine, Haine Ghislain, Matignon Denis, Maschke Bernhard (2022) Structure-preserving discretization of a coupled Allen-Cahn and heat equation system. IFAC-PapersOnLine 55(18):99–104. Montreal, Canada.

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