# 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?

Cheers

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.
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,
Timm

tanx a lot Timm for your help
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.

Hello,