Structure-preserving discretization of Allen-Cahn and Cahn-Hilliard equations, as port-Hamiltonian systems

Abstract

Water desalination is a critical process and can be achieved in different ways. One of them is eutectic freeze crystallisation, this method seems more energy efficient due to the difference between the latent heat of fusion and the latent heat of vaporisation of water. The question then arises as to how to model, simulate and control such a system. Because of the thermodynamic nature of the freezing process, the port-Hamiltonian framework seems useful for it preserves the structure and extensive variables of the system. Moreover, the sharp interface between the solid and the liquid makes the modelling more difficult, therefore one needs to use a phase field method in order to approximate the sharp interface by a diffuse one. In this document, the goal is to compute the equations of Allen-Cahn and Cahn-Hilliard using the pHs formalism by spatially discretizing it using the Partitioned Finite Element Method.