Density in equilibrium distribution function

Lattice Boltzmann Method LBM: Theory
#1

Hi,
In the common Equilibrium distribution Function, we do not see the term rho (density). But in dimensionless form of the distribution function (sometimes referred as the normalized Maxwell’s distribution function) it comes up.

Common form= (4pic^2)((m/2kTpi)^3/2)(exp(-m.c^2/2kTpi))

Normalized form= (rho/(2*pi/3))(exp(-3(c-u)^2/2))

(U=c-u, c=micro speed, u=fluid bulk speed)

Note that there are other types of normalized form. Does anybody know the mathematical procedure? I greatly appreciate it…

#2

Hello Hammed. All it depend what you want to represent whit this term. Generally this term is used for density but in Shallow Water model is used for the water deep. In Donald A. Mcquarrie. Statistical Mechanics. 2 nd edition, 2007 can you see something like that. Regards

#3

Dear Jairus
thank you for the note. I would take a look at that book.