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Paper WeS2M.1

Yaghi, Mohammed (Univ Lyon, Université Claude Bernard Lyon 1, CNRS), Couenne, Francoise (Univ Lyon, Université Claude Bernard Lyon 1), Galfré, Aurélie (Univ Lyon, Université Claude Bernard Lyon 1, CNRS), Lefevre, Laurent (Univ. Grenoble Alpes), Maschke, Bernhard (Univ Claude Bernard of Lyon)

Port Hamiltonian Formulation of the Solidification Process for a Pure Substance: A Phase Field Approach

Scheduled for presentation during the Regular Session "Distributed Parameter Systems" (WeS2M), Wednesday, July 27, 2022, 13:00−13:20, 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 March 28, 2024

Keywords Distributed Parameter Systems, Non Linear Control Systems

Abstract

In this paper we suggest a Port Hamiltonian model of the solidification process of water, using the phase field approach. Firstly, the Port Hamiltonian formulation of the dynamics of the phase field variable, governed by the Allen-Cahn equation, is recalled. It is based on adding to the phase field variable, its gradient, and extending the system with its dynamics. Secondly, the model is completed by the energy balance equation for the heat conduction and the complete Port Hamiltonian model is derived. Thirdly a Algebro-differential Port Hamiltonian representation is suggested, where the Port Hamiltonian system is defined on a Lagrangian submanifold, allowing to use directly the variables defining the thermodynamical data.

 

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