Pressure laws and fast Legendre transform

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00424061
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Submitted on : Sunday, January 3, 2010 - 10:06:15 AM
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Philippe Helluy, Hélène Mathis. Pressure laws and fast Legendre transform. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2010, 21 (4), pp.745-775. ⟨10.1142/S0218202511005209⟩. ⟨hal-00424061v2⟩

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