A second-order multi-fluid model for evaporating sprays
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) no. 5, pp. 931-963.

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.

DOI : https://doi.org/10.1051/m2an:2005041
Classification : 35Q35,  65Z05,  76T10
Mots clés : moment method, sectional method, sprays, evaporation, multi-fluid
     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},
     pages = {931--963},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {5},
     year = {2005},
     doi = {10.1051/m2an:2005041},
     zbl = {1075.35048},
     mrnumber = {2178568},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an:2005041/}
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) no. 5, pp. 931-963. doi : 10.1051/m2an:2005041. http://www.numdam.org/articles/10.1051/m2an:2005041/

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