Hello, I'm doing some work to get permeability in 2D porous media by LBM.
And I'm considering Zou/He pressure BC in my inlet/outlet, because my geometry may not be periodic (I read some papers about effective body force for pressure gradient BCs and understood that method can be used in periodic geometry).
To validate my LBM code, I'm doing compare analytic solution and numerical solution about Poiseuille flow between plates. And I saw weird phenomena.
When, inlet velocity reach to outlet, velocity in outlet become greater than inlet. So, magnitude of velocity seems to propagate outlet to inlet. (=magnitude of velocity seems to be reversed)
I guess this phenomena comes from Zou/He pressure BCs. Because unknown population of inlet (or outlet) comes from known population, when population from inlet(or outlet) reaching to outlet( or inlet), flow should be reversed.
So, my question is "Is this phenomena right?/ Should I consider streaming from neighboring node in inlet/outlet?". Because, in my common sense, flow formed opposite direction to pressure gradient quite seems weird(It is creeping flow). (But it shows good result when comparing analytic solution)
And when I'm not considering streaming from neighboring node(just do overwriting to initial value), result was not good and fully developed flow can not be formed.
I needs you guess advice.
Thank you for your reading.
Dear Hyeonseong Jo
You've probably made a mistake in coding the streaming step. In fact, if the Zou/He boundary conditions are applied correctly, there will be no problem.
My advice to you is to check your code more carefully.
I really appreciate for your reply Bijan Moradi
I'll check my code in streaming step more carefully.
But, to explain a little more about my phenomena, I made this code using matlab and circshift function is used in streaming step.
My phenomena is attached in PNG files(Yellow color means much greater velocity).
So, in the beginning, inlet(=left) has velocity value by pressure boundary condition and outlet(=right) has zero velocity. (figure Inlet_to_outlet.PNG)
And when velocity from inlet reach to outlet, velocity in outlet become greater than inlet. (figure Outlet_to_inlet.PNG)
The reason I guess this phenomena comes from Zou/He BCs is form of equation to find unknown population. If we see the outlet node,
rho = rho_out (specified value);
f_4 = f_2 - 2/3*rho*ux
f_8 = f_6 + 1/2*(f_3 - f_5) - 1/6*rho*ux
f_7 = f_9 + 1/2*(f_5-f_3) - 1/6*rho*ux
% 7 3 6
% 4 1 2
% 8 5 9
above equation is used for unknown population of outlet node. I thought when f_2, f_6, f_9 from inlet node are reaching to outlet node by outlet node, this reversing phenomena can be occurred. Because f_2, f_6, f_9 value from inlet are much bigger than initial value of f_2, f_6, f_9.
The reason inlet velocity becomes small can be explained similar way.
Thank you for your reading.
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