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Internal Report

An inventory of Lattice Boltzmann models of multiphase flows

Author Document Type Year Download File size
Minh Do-Quang, Massimo Vergassola, Erik Aurell Technical report 2000 Download
Id
ISSN 0348-467X
ISRN KTH/MEK/TR--01/

Abstract

This document reports investigations of models of multiphase flows using Lattice Boltzmann methods. The emphasis is on deriving by Chapman-Enskog techniques the corresponding macroscopic equations. The singular interface (Young-Laplace-Gauss) model is described briefly, with a discussion of its limitations. The diffuse interface theory is discussed in more detail, and shown to lead to the singular interface model in the proper asymptotic limit. The Lattice Boltzmann method is presented in its simplest form appropriate for an ideal gas. Four different Lattice Boltzmann models for non-ideal (multiphase) isothermal flows are then presented in detail, and the resulting macroscopic equations derived. Partly in contradiction with the published literature, it is found that only one of the models gives physically fully accept-able equations. The form of the equation of state for a multiphase system in the density interval above the coexistance line determines surface tension and interface thickness in the diffuse interface theory. The use of this relation for optimizing a numerical model is discussed.