Implementing gravity in shear flow simulation

Hi, everyone.
I’m trying to implement the body force (gravitational force, precisely). I have already implemented a ‘classical’ BGK simulation of both Poiseuille and shear flow. And it works ok. Now, for the implementation of body force, I used the method proposed by Guo et. al. (2002), with the modification of both collision term and velocity…
I have the following problem. If I set the top and bottom walls to be zero-velocity, add the periodic boundary along the horizontal direction (along x axis) and set the gravity force to be only along the horizontal axis, I obtain a velocity profile close to that of Poiseuille flow. And I think that it is correct.

But, when I try to set a velocity profile on inlet and/or outlet, (never mind if it is the Poiseuille velocity profile or shear flow condition), I don’t obtain correct velocity profile…
And I need this because I want to simulate shear flow with additional body force acting on the fluid.
I hope that someone here on this forum has been working on similar simulations and can help me with some useful tips or a solution for my problem.
Thank you in advance !