# Fluctuating Lattice Boltzmann

hey guys, i’ve a couple of questions about how choosing the correct parameters while carrying out a fluctuating lattice boltzmann simulation.
In particular, once i choose my dx and dt and therefore the speed of sound how do i convert kB*T from physical units to lattice units?
i hope i’ve been clear…

I don’t know, but here is quite a nice thesis which may be of use http://www.mpip-mainz.mpg.de/theory/Theses/Thesis_Documents/50/thesis

Actually, although I don’t know about fluctuating LBE, RT in kinetic theory (which can be written in terms of Boltzmann’s constant) has dimensions of speed^2, so RT in numerical scalings would be RT/c/c where c=dx/dt is the grid spacing divided by the timestep… Note that in standard LB, one generally uses an equation of state P=rho(RT)’=rho/3, where (RT)’ means RT in lattice units. That is, (RT)’=(RT)/c/c=1/3.This is the most stable choice but it means RT depends on the scaling used. In other words, it’s not really a physical equation of state. It is possible to adjust RT according to physical values of a gas but you need to be careful of numerical stability (c might have to be quite large).

If i understood well, once i choose Time and space scalings…and therefore Cs i Also fix RT’.
Since termale fluctuations are proportional to kBT (RT’) this means that it is likely i’m simulating a non realistic temperature…
I think i have to study a bit more from ladd and succi papers.

Dear pleb01, apparently the link is not available anymore. Could you provide the author+year, please?

I interpreted Ulf Schillers PhD thesis from 2008 in such a way, that the boundary condition is thermalized as well. By my conception, the boundary condition should then vary between slip and no-slip.
Is that true? If so: How?
Thank you