Poisseulle by LBM and analytical solution

Lattice Boltzmann Method LBM: Theory
#1

Dear All
i just wrote a code for poisseulle flow based on Sukop’s pages 56-57 but using Zhaoli Guo’s Method for applying gravity
this is my result after 45000 iteration it should become steady state :smiley:

and i use following formula for calculating analytical solution
tao=1;
xAnal=0:12;
xAnal=xAnal-6;
g=1.102e-3
uAnal=g/(21/3(tao-1/2)).*(6.0^2-xAnal.^2);
Result is here:
j --------- i---------v analytical---------------v LBM
1--------1-------------0--------------------------- 0
1---------2---------0.0364----------0.0205543066552522
1---------3---------0.0661----------0.0554192958825788
1---------4---------0.0893----------0.082565027158221
1---------5---------0.1058----------0.101974768435595
1---------6---------0.1157----------0.113629920602504
1---------7---------0.1190----------0.117516656267497
1---------8---------0.1157----------0.113629920602504
1---------9---------0.1058----------0.101974768435595
1---------10-------0.0893----------0.082565027158221
1---------11-------0.0661----------0.0554192958825787
1---------12-------0.0364----------0.0205543066552522
1---------13--------0------------------------------0

as u see there is a difference between analytical solution and my LBM code, is this mean there was a bug in my code
and is this possible we get result absolutely equal to analytical solution? please Help me

Regards
Sajad

     0
#2

Hi,
I have done similar work on Poisseulle flow. I think your numerical result is not very accurate.
How about your Reynolds number? If it is high, I suggest you to thicken your grid. Maybe it is the resulation of the grid that influences your result.

Regards

#3

Dear JJlei
thank u for your reply.
i use Sukop method for gravity implication(u+tao*F/rho & F=mg=g) and result improved in comparision with above results. Result yet had a little difference with analytical. i simulate Poisseule flow in the case of 11mm thick with dx=1mm what is your opinion about this resolution and this thickness?

thanks in advance
Sajad

#4

Hello,

You will always have the difference with the analytical solution while using BGK and BB nodes. Please take a look at the number of papers (I. Ginzburg) or my thesis available at lbmethod.org

Hopefully it will help,
Alex