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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.

Information

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

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