Dear Seyed Ali-Hosseini,

In Multiphase LBM, I am using p= rho*c_s^2 + c_0*0.5* psi^2, the other term is for accounting interactive forces to the LBM for incorporating phase change. Will it (the other term) contribute in dimensionalising the pressure?

Dear Debashis, the second term in your formula (which, by the way, is missing the coupling constant g) is a pressure too. First of all because you are adding it to a term which is a pressure. You can verify that even by performing a dimensional analysis, remembering the the effective mass psi has the dimensions of a density [Kg/m^3]. Therefore what Dr. Seyed Ali Hosseini stated in his clear answer remains valid.

Best Regards,

Ernesto

Thank you Ernesto for your input.

Interesting question

You may want to refer to this ref. There is a table converting lattice units to physical units.

Feng, Y. T., Han, K. and Owen, D. R. (2007), Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues. Int. J. Numer. Meth. Engng., 72: 1111-1134. doi:10.1002/nme.2114

You can use the equation of state P=rho*c_s^2 to convert the density to dimensionless pressure. But of course you need a base density/pressure about which you are calculating the density/pressure deviations. To convert it to physical scale, you will be needing dt and dx which comes from scaling.

Hi

Actually, I know it is a late reply to this question, however, I think the approach mentioned by other researchers is only valid for a single component and single phase flow. For multiphase flow in which an EOS is utilized, you should set a temperature and specify the type of fluid you are using by setting the two parameters a and b. In addition, there are some relation between a and b and critical parameters. Therefore, It would be a simple scaling from what you calculated in LB unit, the critical value in LB unit, and real critical pressure value in thermodynamic table of the given fluid. It would be something like this: P(real)=P(critical-real)*P (calculated in LB)/ P(critical in LB).

I hope this help.

Meysam

For unit conversation, please look at the book of Timm Krüger and the implementation within OpenLB, which follows Timm's notations. Timm is giving a lecture on it at our next Spring School in Berlin (see www.openlb.net).