[ESPResSo-users] No conservation of momentum/mass in LBM ??

[Wink, Markus]

Hello Everybody,

 

so far, in the LBM scheme only the body force is implemented and no velocity/pressure boundary condition. So I was thinking on a way of mimicking a “velocity boundary” condition without changing the source code. I am aware that one should, as a proper approach, using Zou/He boundary conditions and adjusting the distribution functions according to the boundary conditions.

 

For that I have constructed a channel with rectangular cross section and put the fluid inside. Furthermore, two rhomboids where put inside, one at the inlet of the channel, one at the outlet. The cross section of the two rhomboids is equal to the cross section of the channel, furthermore they have a constant velocity v0.

My idea was, that, since the no-slip boundary condition is implemented, I force the fluid nodes adjacent to the rhomboids to have a constant velocity, thus achieving constant velocity inlet/outlet condition.

 

As a result I achieve a poiseuille profile in the middle of the channel (fully developed flow after inlet/outlet effects). The qualitative pressure gradient looks proper, too.

Nevertheless, the maximum velocity is not the same as I expected (factor 3 to the expected one).

I have checked the mean velocity. I would expect, that the mean velocity of the fluid should be the velocity v0 of the rhomboid (due to mass/momentum conservation), I get less (10 %).

 

What is wrong with my idea stated here? Obviously, something is not correct, but I have no idea, what the reason for that is. Where does the momentum vanish?

 

Does anybody have an idea?

 

Sincerely,

 

Markus