Pressure laws and fast Legendre transform

Philippe Helluy (1) , Hélène Mathis (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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.

Mots clés: phase transition; fenchel transform; tabulated pressure laws; thermodynamics

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Helluy, Hélène Mathis. Pressure laws and fast Legendre transform. Mathematical Models and Methods in Applied Sciences, 2010, 21 (4), pp.745-775. ⟨10.1142/S0218202511005209⟩. ⟨hal-00424061v2⟩