Trouble in implementation of D2Q9 code in fortran for velocity driven Poiseuille flow


I’m trying to implement LBM for velocity driven poiseuille flow (zero pressure gradient) with a D2Q9 model. A free stream velocity is applied at the inlet and full-bounce-back boundary conditions at top and bottom walls. As of now, I haven’t specified any specific boundary condition for the outlet but the streaming process ensures a zero gradient condition there. My problem is that the final maximum value of the x-direction velocity is smaller than the value I’ve specified as the magnitude of the free-stream velocity. The analytical solution says Umax should be 1.5 times U(free stream). Is this because I haven’t specified any boundary condition for the outlet? The problem persists even if I give periodic boundary condiditon at inlet and outlet. Your help is really appreciated.

Thanks in advance and in anticipation,

Aswathy Nair K.
IIT Madras


The bounce back boundary condition for 2D corners is not needed anymore.

I suggest you to read this paper:
On pressure and corner boundary conditions with two lattice Boltzmann construction approaches

Mathematics and Computers in Simulation
Volume 84, October 2012, Pages 26–41

which also available
and the details you are asking are presented there.

Good luck