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Simulation of free boundaries in flow systems by lattice-gas models

Published online by Cambridge University Press:  21 April 2006

P. Clavin ,
P. Lallemand ,
Y. Pomeau  and
G. Searby
P. Clavin
Affiliation:
Laboratoire de Recherche en Combustion, Centre de St Jérôme, 13397 Marseille Cedex 13, France
P. Lallemand
Affiliation:
Laboratoire de Physique de l'Ecole Normale Supérieure, 24 rue Lhomond 75231 Paris Cedex 05, France
Y. Pomeau
Affiliation:
Laboratoire de Physique de l'Ecole Normale Supérieure, 24 rue Lhomond 75231 Paris Cedex 05, France
G. Searby
Affiliation:
Laboratoire de Recherche en Combustion, Centre de St Jérôme, 13397 Marseille Cedex 13, France
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Abstract

It has been recently proved that lattice-gas models with Boolean particles can provide a very powerful method to study viscous flows at moderate Reynolds and small Mach numbers (d'Humières, Pomeau & Lallemand 1985; Frisch, Hasslacher & Pomeau 1986; d'Humières & Lallemand 1986). We present here algorithms for an extension of these models to provide a simple and efficient way to simulate a large variety of flow problems with free boundaries. This is done by introducing two different types of particles that can react following a specific kinetic scheme based on autocatalytic reactions. In order to check the powerful character and the reliability of the method we also present preliminary results of two-dimensional computer simulations concerning problems ranging from the competition between molecular diffusion and turbulent mixing in flows presenting a Kelvin-Helmholtz instability to the spontaneous generation of turbulence in premixed flame fronts subject to the Darrieus-Landau instability. The dynamics of an interface developing a Rayleigh-Taylor instability is also considered as well as some typical problems of phase transition such as spinodal decomposition and the nucleation process.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 188 , March 1988 , pp. 437 - 464
Copyright
© 1988 Cambridge University Press

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