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

• Published in: Journal of fluid mechanics Vol. 188; pp. 437 - 464
• Main Authors: Clavin, P., Lallemand, P., Pomeau, Y., Searby, G.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.03.1988
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Physics; Fluid mechanics; Free boundary; Kelvin Helmholtz instability; Digital simulation; Rayleigh Taylor instability; Modeling; Lattice gas
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112088000795

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.