Lattice BGK constraints.....

Lattice Boltzmann Method LBM: Theory
#1

I had gone through sukops book and came a cross a point in page number 66 which said that maximum velocity should be limited to 0.05 lu/ts elsewhere it is also mentioned that it should less than 0.1 lu/ts . can someone explain what is the basis for this constraint? what is the maximum range of reynolds number that this model can solve sucessfully?

Having gone through the matlab code for lid driven cavity i wanted to try out poiseulle flow wid pressure boundary conditions but for a given random problem it was very difficult to keep the maximum velocity down to the above value. so it would be of good help if someone annswered my above issues and gave me 2 things?

  1. actual physical units of lid driven cavity problem solved in code?
  2. A random poiseullie flow problem anyone has solved before with pressure boundary conditions having physical units?

Regards
Stanley

#2

Hello Stanley,

I too have wondered about this velocity constraint and thus far have found no conclusive answer in literature. I do, however, suspect it has to do with the small Mach number expansion that is used in the derivation of the LBGK equation, thereby essentially limiting the flow to the incompressible regime, or M < 0.3
This will give a maximum lattice velocity of u[sub]max[/sub] = 0.3 c[sub]s[/sub] = 0.3 * sqrt(1/3) = 0.1732 lu/ts

This does not yet explain the further restriction to 0.1; maybe there is someone with a better explanation.

Elrohir