The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame 60 (1985) 15-28] exposed in [F. Laurent and M. Massot, Combust. Theory Model. 5 (2001) 537-572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each section ensuring the exact conservation of two moments (as opposed to only one moment used in the classical approach). A corresponding second-order numerical scheme, with respect to space and droplet size variables, is also introduced and can be proved to be positive and to satisfy a maximum principle on the velocity and the mean droplet mass under a suitable CFL-like condition. Numerical simulations have been performed and the results confirm the accuracy of this new method even when a very coarse mesh for the droplet size variable (i.e.: a low number of sections) is used.
@article{M2AN_2005__39_5_931_0,
author = {Dufour, Guillaume and Villedieu, Philippe},
title = {A second-order multi-fluid model for evaporating sprays},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {39},
year = {2005},
pages = {931-963},
doi = {10.1051/m2an:2005041},
mrnumber = {2178568},
zbl = {1075.35048},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2005__39_5_931_0}
}
Dufour, Guillaume; Villedieu, Philippe. A second-order multi-fluid model for evaporating sprays. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) pp. 931-963. doi : 10.1051/m2an:2005041. http://gdmltest.u-ga.fr/item/M2AN_2005__39_5_931_0/
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