Recently, I worked on 2D Poiseuille flow simulation to investigate different boundary conditions.
I used constant body force in one case and pressure boundary condition (Zou and He method) in the other.
The results are pretty similar. So, what is the difference between these two methods?
Do you have any idea about the benefit of each of these deriving forces?

The body force boundary is periodic, and hence represents an infinitley long/repeating domain, where velocity at the boundaries can have non-zero x and y (and z) components. Zou & He pressure boundaries give a non-periodic domain with the tangential component of velocity fixed at zero. Choice of one or the other depends on the problem to be modeled.

Thanks for your reply. I have another question. Suppose we are going to model a vertical flow in a pipe using pressure boundary condition. Since gravity force also affects the flow (since the pipe is vertical), should I use both boundary conditions in order to have a reliable answer?

That is really for you to decide. There are situations where considering both might be useful, just like there are situations where the effect of gravity is so much bigger then the pressure bc’s its not worth considering (or vice versa).

I totally agree. Otherwise, one can see gravity as an additional pressure gradient (which is not entirely correct but a good approximation). Just have a look at the Navier-Stokes equations and combine the pressure gradient and force density terms. The flow cannot distinguish between an externally applied pressure gradient and an external body force density. However, in LBM, a pressure gradient leads to a density gradient (a constant body force does not) which in turn can cause problems if the density gradient becomes too large.

I investigate this problem.my problom has two boundary condition (upper and lower) which they are stationary. two other boundary conditions are in two diffrent pressure .I have a question.can I use two boundary condition constant pressure with force term at collision part(both of them together)?