I’m implementing very simple lattice kinetic scheme (LBM with tau = 1), and I’ve ran into some strange problems. I’m following Orestis Malaspinas’ thesis, (http://biblion.epfl.ch/EPFL/theses/2009/4505/EPFL_TH4505.pdf page 47).
Imagine hypothetical problem: Steady homogenous fluid, with periodic boundary conditions. A constant force is applied in one direction. I believe, that the fluid should be constantly accelerating. But if I implement this numerical scheme, it does not move. I will explain things in terms of LBM, although I’m using the kinetic scheme.
At the beginning, all the particle velocities are the same, and set to equilibrium ones, with equilibrium f^eq + tau F (that means, including the force term). The velocity is computed, and according to Malaspinas’ thesis, equation 2.118, the velocity is corrected: u = u(computed) + g/2. This velocity is zero. After first streaming step, all particle distributions remain the same, so does the corrected velocity, the fluid does not move.
Is there any difference in implementing force term, in lattice kinetic scheme?
I tried to disable the velocity correction, when simulation Poiseuille flow, I get some parabolic profile, but the velocity seems to rise indefinitely. Maybe the problem is, that the initial distribution should not include the force term? I tried to set initial velocity to -g/2 (assuming, it will cancel the effect of force term). In Poiseuille case, it moves the fluid a bit, but the velocity is very small.
I’m a bit confused with all this
Thanks for any ideas,