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Issue ESAIM: Proc.
Volume 28, 2009
CEMRACS 2008 - Modelling and Numerical Simulation of Complex Fluids
Page(s) 117 - 134
DOI http://dx.doi.org/10.1051/proc/2009042
Published online 23 November 2009

ESAIM: Proc., 2009, Vol. 28, pp. 117-134
DOI: 10.1051/proc/2009042

Numerical simulations of low Mach compressible two-phase flows: Preliminary assessment of some basic solution techniques

Benjamin Braconnier1, Jeu-Jiun Hu2, Yang-Yao Niu3, Boniface Nkonga4 and Keh-Ming Shyue5

1  GLAIZER Group innovation agency, France,
    e-mail: benjamin.braconnier@glaizer.com
2  Department of Information Management, Shu-Te University, Taiwan,
    e-mail:jjhu@mail.stu.edu.tw
3  Department of Mechanical and Aerospace Engineering, Chung Hua University, Taiwan,
    e-mail: yyniu@chu.edu.tw
4  Department of Mathematics, University of Nice, France,
    e-mail: Boniface.Nkonga@unice.fr
5  Department of Mathematics, National Taiwan University, Taiwan,
    e-mail:shyue@math.ntu.edu.tw, Corresponding author


Published online: 23 November 2009

Abstract
The objective of this paper is to give a preliminary assessment of several existing approaches (compressible or incompressible, preconditioned or not preconditioned) to the numerical simulation of low Mach compressible two-phase flow problems in more than one space dimension. We consider a broken dam problem of Martin and Moyce [Philos. Trans. Roy. Soc. London A, 244(1952), pp. 312-324] and a wave breaking problem of Yasuda et al.  [Costal Engineering, 29(1997), pp. 317-346] as our benchmark tests, where the computed results obtained by using the numerical methods can be compared with the laboratory experiments for the basic solution validations.


Résumé
L'objectif de ce papier est d'évaluer la pertinence de plusieurs méthodes dédiées à la simulation numérique d'écoulements à deux phases lorsqu'elles sont utilisées pour approcher des écoulements dont le nombre de Mach est faible. Ces méthodes reposent sur des modèles bidimensionnels gouvernant des fluides compressibles (avec ou sans préconditionnement faible Mach) ou incompressibles. De manière à permettre une validation élémentaire par comparaison entre résultats numériques et expérimentaux, deux tests nous ont servi de référence: l'effondrement d'une colonne d'eau (Martin and Moyce [Philos. Trans. Roy. Soc. London A, 244(1952), pp. 312- 324]) et le déferlement d'une vague (Yasuda et al. [Costal Engineering, 29(1997), pp. 317-346]).



© EDP Sciences, ESAIM 2009


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