ideal gas EOS

Hello Dear all
I am a beginner student in LB and have some questions about it. Can everyone help me?

1-What is the meaning of this sentence?
”LB is a pseudo-compressible solver with the fluid pressure p, given by the following equation of state: p =Cs2 “
LB virtual fluid is an ideal gas? Can I simulate turbulent liquid flows with this approach?


Hello Mirahmadi,

yes you can simulate such flows. The LBM is a method, which asymptotically solves the Navier-Stokes equations. “Asymptotically” means that not the Navier-Stokes equations themselves, but a very similar set of equations are solved. The difference, however, is small. Especially, when you are in a regime where the Mach number and the pressure gradients are not too large, the LBM works very well.
When you have a more closer look at the LB equation (in contrast to the NS equations) you will find that the density is not rho = const, but rho = p / c_s^2. This means that the LB fluid is compressible.
The best thing would be: Read a review article, e. g. this article[/url]. You can also start with Jonas’ [url=]PhD thesis.
You will sooner or later encounter the phrase “Chapman-Enskog analysis”. When you understand this, you understand most of the LB theory.

Hope this helps you a bit,

tanx a lot Timm for your help
i have some questions about your reply:
1-“asymptotically solving of the N-S equations” means using a method similar to Perturbation Theory in PDE solving?

2- “Mach number and the pressure gradients are not too large”
real [physical] Ma No? [or computational Ma. No.]

unforchunetly i sent previous message twice!!
i can not delete this message, Pls delete it.


regarding your two recent questions:
1: asymptotically means that the equation which is solved by the LBM is not exactly the NS equation, but “pretty close to it”. In order to understand that, you could for example have a look at our paper. Read sections II A and II B and also have a look at the cited literature.
2: Mach number in the simulation. Usually, the physical Mach number of your system is pretty small. But in order to save computing time, you can increase it in the numerical model, which introduces so called “compressibility errors”. Be sure that your Mach number is not larger than, say, 0.2 in your model. If it is too small, you waste a lot of computing time. But you will see that for yourself when you simulate your first physical systems.