Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 5, p. 1029-1054

In the present work we investigate the numerical simulation of liquid-vapor phase change in compressible flows. Each phase is modeled as a compressible fluid equipped with its own equation of state (EOS). We suppose that inter-phase equilibrium processes in the medium operate at a short time-scale compared to the other physical phenomena such as convection or thermal diffusion. This assumption provides an implicit definition of an equilibrium EOS for the two-phase medium. Within this framework, mass transfer is the result of local and instantaneous equilibria between both phases. The overall model is strictly hyperbolic. We examine properties of the equilibrium EOS and we propose a discretization strategy based on a finite-volume relaxation method. This method allows to cope with the implicit definition of the equilibrium EOS, even when the model involves complex EOS's for the pure phases. We present two-dimensional numerical simulations that shows that the model is able to reproduce mechanism such as phase disappearance and nucleation.

DOI : https://doi.org/10.1051/m2an/2011069
Classification:  76T10,  76N10,  65M08
Keywords: compressible flows, two-phase flows, hyperbolic systems, phase change, relaxation method
@article{M2AN_2012__46_5_1029_0,
author = {Faccanoni, Gloria and Kokh, Samuel and Allaire, Gr\'egoire},
title = {Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {46},
number = {5},
year = {2012},
pages = {1029-1054},
doi = {10.1051/m2an/2011069},
zbl = {1267.76110},
mrnumber = {2916371},
language = {en},
url = {http://www.numdam.org/item/M2AN_2012__46_5_1029_0}
}

Faccanoni, Gloria; Kokh, Samuel; Allaire, Grégoire. Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 5, pp. 1029-1054. doi : 10.1051/m2an/2011069. http://www.numdam.org/item/M2AN_2012__46_5_1029_0/

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