Numerical analysis of eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 3, p. 431-468

The purpose of this article is the analysis and the development of Eulerian multi-fluid models to describe the evolution of the mass density of evaporating liquid sprays. First, the classical multi-fluid model developed in [Laurent and Massot, Combust. Theor. Model. 5 (2001) 537-572] is analyzed in the framework of an unsteady configuration without dynamical nor heating effects, where the evaporation process is isolated, since it is a key issue. The classical multi-fluid method consists then in a discretization of the droplet size variable into cells called sections. This analysis provides a justification of the “right” choice for this discretization to obtain a first order accurate and monotone scheme, with no restrictive CFL condition. This result leads to the development of a class of methods of arbitrary high order accuracy through the use of moments on the droplet surface in each section and a Godunov type method. Moreover, an extension of the two moments method is proposed which preserves the positivity and limits the total variation. Numerical results of the multi-fluid methods are compared to examine their capability to accurately describe the mass density in the spray with a small number of variables. This is shown to be a key point for the use of such methods in realistic flow configurations.

DOI : https://doi.org/10.1051/m2an:2006023
Classification:  35L05,  65L20,  76T10
Keywords: spray, evaporation, multi-fluid method, kinetic schemes
@article{M2AN_2006__40_3_431_0,
author = {Laurent, Fr\'ed\'erique},
title = {Numerical analysis of eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {40},
number = {3},
year = {2006},
pages = {431-468},
doi = {10.1051/m2an:2006023},
zbl = {1160.76380},
zbl = {pre05122981},
mrnumber = {2245317},
language = {en},
url = {http://www.numdam.org/item/M2AN_2006__40_3_431_0}
}

Laurent, Frédérique. Numerical analysis of eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 3, pp. 431-468. doi : 10.1051/m2an:2006023. http://www.numdam.org/item/M2AN_2006__40_3_431_0/

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