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Port Hamiltonian systems with moving interface: the two-phase Stefan problem

Abstract : In this paper we propose a port Hamiltonian formulation of the two-phase Stefan problem. This problem describes the evolution of a pure material which is at two different states of matter: liquid and solid. This is a parabolic distributed parameter system which possesses a sharp moving interface. The two-phase Stefan problem results from the interconnection of two heat conduction equations at the interface position. The interface dynamics is governed by an ordinary differential equation. The port Hamiltonian formulation relies on the introduction of color functions which identify the liquid and the solid states. The contribution of this paper concerns the formulation of the two-phase Stefan problem as a sharp interface port Hamiltonian system. A thermodynamic-based modeling approach is considered to provide a physical insight on the proposed model.
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Contributor : Francoise Couenne <>
Submitted on : Monday, December 21, 2020 - 11:47:36 AM
Last modification on : Wednesday, January 6, 2021 - 3:28:14 AM


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  • HAL Id : hal-03084647, version 1



Benjamin Vincent, Françoise Couenne, Laurent Lefèvre, Bernhard Maschke. Port Hamiltonian systems with moving interface: the two-phase Stefan problem. 2020. ⟨hal-03084647⟩



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