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Pressure laws and fast Legendre transform

Philippe Helluy 1, Hélène Mathis 1

(14/10/2009)

In this paper we investigate algorithms based on the Fast Legendre Transform (FLT) in order to compute tabulated equation of state for fluids with phase transition. The equation of state of a binary mixture is given by an energy minimization principle. According to the miscible or immiscible nature of the mixture, the energy of the system is either a convex envelope or an inf-convolution of the energies of the phases. Because these operations are closely linked to the Legendre transform, it is possible to construct $O(N)$ algorithms that compute efficiently these operations, where $N$ is the number of points in the table. In addition, it appears that the natural mathematical tool for studying mixture thermodynamics in the Legendre space is the max-plus algebra theory.

1 :	Institut de Recherche Mathématique Avancée (IRMA)
	CNRS : UMR7501 – Université de Strasbourg

Domaine

:

Mathématiques/Equations aux dérivées partielles

Mots Clés : phase transition – fenchel transform – tabulated pressure laws – thermodynamics

hal-00424061, version 2

http://hal.archives-ouvertes.fr/hal-00424061

oai:hal.archives-ouvertes.fr:hal-00424061

Contributeur : Philippe Helluy <>

Soumis le : Dimanche 3 Janvier 2010, 10:06:15

Dernière modification le : Lundi 22 Mars 2010, 14:38:54