[sbaffini]

Originally Posted by Bottikowski96

I have simulated a 2D laminar channel flow without a forcing term, with no-slip BC and ∂p/∂x=1 (in form of the BC: p(x=0)=length of channel | p(x=l)=0). This delivers the correct results. Then, I tried to run the same benchmark with no-slip BC again, but instead of the above pressure BC, I used a forcing term of f=(1,0). But then I get a velocity of zero in both directions in the entire domain. Why is that the case?

The periodicity part is fundamental here. While a pressure bc equivalent to the linear pressure drop can be obtained, the actual bc can't really be that one on pressure alone on both inlet and outlet boundaries.

Periodicity gives the correct bc for velocity and the periodic pressure part. If you don't want to use periodicity you need to amke the flow develop naturally in a sufficiently long tube. In that case you just use a given velocity inlet and a pressure outlet.

[LuckyTran]

Please clarify your entire boundary conditions for both pressure and velocity. It works means you get a solution that looks like what? It looks like fully developed and looks exactly like the DNS results or does it look like an entirely different flow but is non-zero velocity and so you are happy with any result? In the second case you get a zero velocity so you are instantly unhappy, that is understood.

You use pressure at inlet and outlet without a forcing term. What about the velocity? It should be periodic for velocity.

You apply a forcing term. What is your BC for pressure? And what is the BC for velocity? It should be periodic for pressure and periodic for velocity.

I have simulated with pressure jump condition and forcing term in 2D and 3D for both cases and I can confirm it works. I know that the others responding to this thread have done similar cases as well. And there is also quite a breadth of literature including the paper you cited that shows it has been done before. It's not a hoax. We're really just trying to help you figure out why it doesn't work for you but does work for everybody else. Make sure you are using periodic conditions!

[FMDenaro]

And there is a physical difference between inlet/outlet conditions and periodicity. The former simulates a spatial evolving BL, the latter the temporal evolving BL.

I suppose a steady Poiseuille flow is obtained by fixing just the pressure at inflow and outflow, maybe this is the problem that “works”.