Bendimerad-Hohl, Antoine, Amine (ISAE Supaero), Haine, Ghislain (Institut Superieur de l’Aeronautique et de l’Espace), Matignon, Denis (ISAE), Maschke, Bernhard (Univ Claude Bernard of Lyon)

Structure-Preserving Discretization of a Coupled Allen-Cahn and Heat Equation System

Scheduled for presentation during the Regular Session "Distributed Parameter Systems" (WeS2M), Wednesday, July 27, 2022, 13:20−13:40, Lassonde M-2103

IFAC Workshop on Thermodynamic Foundations of Mathematical Systems Theory, July 24-27, 2022 , Montreal, Canada

This information is tentative and subject to change. Compiled on April 25, 2024

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.