LB in a sealed 2D box

Lattice Boltzmann Method LBM: Theory
#1

Greetings to everyone!

It is so nice to have a forum dedicated to a particular numerical method! My name is Yan, I made my first foray into LB a couple of months ago. I have this question that keeps bugging me.

While learning the method, I inevitably stumbled upon this website and downloaded the sample Matlab scripts. I used a 2D script and modified it to account for the external force term in a manner described in Jonas Latt’s PhD thesis (eqn. 2.74). It worked well for the Poiseuille’s flow with 2 lateral solid walls and open inlet/outlet and a constant force parallel to the flow direction. But then I made all 4 walls solid (with the bounce-back conditions). In this case the method does not converge. I would expect the velocity to be zero and the pressure (or density) to increase linearly from the “inlet” to the “outlet” so that its constant gradient cancels out the force term. Instead I have velocity oscillations that never relax to zero. So the question is as usual - why is that? Is there some intricate LB detail that I am missing here that prohibits one from solving such a case?

Sincerely,
Yan

#2

Hello,

for how long did you let your simulation run? My guess is that at some point it will relax to a zero velocity state, but it will take a very very very long time (depending on the Re of course).

Orestis

#3

Thank you for your reply, Orestis! You were right, I just had to wait long enough and all the oscillations are gone and the density gradient exactly counterbalances the gravity term. I feel like I am being overly suspicious about the LB and expect some non-physical behavior because I do not understand it fully yet :slight_smile:

Yan