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Journal Articles Mathematical Models and Methods in Applied Sciences Year : 2010

Pressure laws and fast Legendre transform


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.
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Dates and versions

hal-00424061 , version 1 (14-10-2009)
hal-00424061 , version 2 (03-01-2010)



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⟩
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