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.
Keywords: moment method, sectional method, sprays, evaporation, multi-fluid
@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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {931--963},
year = {2005},
publisher = {EDP Sciences},
volume = {39},
number = {5},
doi = {10.1051/m2an:2005041},
mrnumber = {2178568},
zbl = {1075.35048},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2005041/}
}
TY - JOUR AU - Dufour, Guillaume AU - Villedieu, Philippe TI - A second-order multi-fluid model for evaporating sprays JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 931 EP - 963 VL - 39 IS - 5 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2005041/ DO - 10.1051/m2an:2005041 LA - en ID - M2AN_2005__39_5_931_0 ER -
%0 Journal Article %A Dufour, Guillaume %A Villedieu, Philippe %T A second-order multi-fluid model for evaporating sprays %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 931-963 %V 39 %N 5 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2005041/ %R 10.1051/m2an:2005041 %G en %F M2AN_2005__39_5_931_0
Dufour, Guillaume; Villedieu, Philippe. A second-order multi-fluid model for evaporating sprays. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 5, pp. 931-963. doi: 10.1051/m2an:2005041
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