Issue
EPL
Volume 86, Number 2, April 2009
Article Number 24005
Number of page(s) 6
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
DOI http://dx.doi.org/10.1209/0295-5075/86/24005
Published online 06 May 2009
EPL, 86 (2009) 24005
DOI: 10.1209/0295-5075/86/24005

Continuum free-energy formulation for a class of lattice Boltzmann multiphase models

M. Sbragaglia1, H. Chen2, X. Shan2 and S. Succi3

1   Department of Physics and INFN, University of Tor Vergata - Via della Ricerca Scientifica 1, 00133 Rome, Italy, EU
2   EXA Corporation - 55 Network Drive, Burlington, MA 01803, USA
3   Istituto per le Applicazioni del Calcolo CNR - Viale del Policlinico 137, 00161 Rome, Italy, EU

sbragaglia@roma2.infn.it

received 29 January 2009; accepted in final form 30 March 2009; published April 2009
published online 6 May 2009

Abstract
It is shown that the Shan-Chen (SC) model for non-ideal lattice fluids can be made compliant with a pseudo-free-energy principle by simple addition of a gradient force, whose expression is uniquely specified in terms of the fluid density. This additional term is numerically simulated and shown to provide fairly negligible effects on the system evolution during phase-separation. To the best of our knowledge, these important properties of the SC model were not noted before. The approach developed in the present work is based on a continuum analysis: Further extensions, more in line with a discrete lattice theory (SHAN X., Phys. Rev. E, 77 (2008) 066702), can be envisaged for the future.

PACS
47.11.-j - Computational methods in fluid dynamics.
47.45.-n - Rarefied gas dynamics.
02.70.-c - Computational techniques; simulations.

© EPLA 2009