Dimensionless Poiseuille flow

Hello everybody,

I am new to the LBM and also to this forum, so I apologize in advance if this is the wrong place for this thread.

After running and playing with the first examples and tutorials from palabos I’m trying to simulate the development of a Poiseulle flow and the results does not exactly match what I expected.

I implemented it with fluid at rest as initial condition, periodic boundaries on the inflow and outflow and non-slip at the walls, with the pressure gradient acting as a constant body force on the whole fluid.

Considering dimensionless units and using the definition of Re and the Hagen–Poiseuille equation I calculated that the pressure gradient depends on the Re with the relation: (dp/dx) = 64/Re, which then I convert to lattice units by multiplying with (δt^2/δx) (the discrete time and space intervals).
Using that I expected to obtain for large time values a flow with average velocity = 1, and maximun velocity = 1.5 at the center, but I’m off by a factor of 4 (My average velocity is ≈ 0.23). Am I missing something when calculating dp/dx?
I thought that maybe I’m doing something wrong with the discretization…

Any help would be really appreciated.

Thanks in advance!