Shan-chen issues

Lattice Boltzmann Method LBM: Theory
#1

Hi I am trying to simulate water vapour condensating into liquid droplets.

I found a sample Matlab script on this site which claims to use the Shan Chen model:
Phys. Rev. E 47, 1815 - 1819 (1993)
Lattice Boltzmann model for simulating flows with multiple phases and components
[prola.aps.org/abstract/PRE/v47/i3/p1815_1]

Having looked through the sample I fail to see how it actually utillises the method described in this paper. It successfully simulates mixing in a mixture of two fluids clearly exhibiting surface tension. It does however not deal with phase transition. The easiest way of identifying this is by realising that the distrubution function for the subsequent timestep fully depends on rho. Meaning that if a phase doesn’t exist it never will. However phase transition as described in the paper mentioned occurs even with zero rho.

More on the point I am having some troubles successfully implementing the theory in this paper. How does one go about determining all the constants in the equilibrium function:
d_0, D, b and c. I can find u and e_a obviously and I have a suspicion c would be sqrt(3RT) but for the others I do not know.
Hopefully somebody could shed some light on my problem.

Regards,
Aleks

#2

Hi,

There are two different models which are unfortunately both sometimes referred to as “the Shan/Chen model”. The first is a multi-phase model working with a single set of particle populations, and in which you observe phase transitions. The second is a multi-component which works with two, or more, sets of particle populations. The code you are looking at uses the multi-component model.

For a discussion of the Shan/Chen models, I can recommend the book by Sukop and Thorne.

#3

Very helpful thank you. I shall try to get a hold of that book and be sure that I will return with more questions :slight_smile: