Periodic boundary condition in spanwise direction
 

Hello, my friends,
I have a CFD question about periodic boundary condition in the spanwise direction. As we know, the periodic boundary condition can set for streamwise direction, so the quantities can replace from outlet to inlet and vice versa. also, in this direction, we should do a pressure correction to find the pressure drop. now, I wanna know the differences of implementing this BC in spanwise and streamwise direction.
Hope to help me.

I suppose you are considering the flow in a planar channel flow. There is no difference in the streamwise and spanwise direction on both a mathematical and numerical aspects. The only difference is that the constant forcing term (the pressure gradient) acts only in streamwise direction but that does not enter in the BC.s setting.

Thank you, Prof, Denaro
my case is a channel with a 3d cavity on its wall. this cavity is far from spanwise walls (z direction). the channel figure is attached. my big problem is that I found in literature the periodic BC for spanwise. what is the problem for symmetry BC in spanwise?

As happens in the streamwise direction, periodic BC.s in spanwise direction implies that the cavity repeats itself indefinitely therefore you need to prescribe a lenght of periodicity that is suitable for your flow problem.

And the symmetry BC cannot be applied, anymore?

In general, you can set any BC.s that get a mathematycally well posed problem, but you have to set only the type of BC.s that physically fulfill your flow problem...

When I posed symmetry BC, I get some strange circulation in my cavity. is the reason, small length in spanwise direction for symmetry BC?

I cannot say. It could also be a bug. Try to extend the domain in spanwise direction.

are these two cases equal? periodic in spanwise with usual length, symmetry in spanwise with large length?

Formally, symmetry BC implies a mirror symmetry, periodic BC implies that the solution repeats itself after a proper lenght

But, normally if the length in my proble be sufficient, these BCs are the same, actually?

A wide extension of the domain in spanwise direction should driven to similar solutions. But the BC.s are not exactly the same.

Thank you
My last problem. You said we dont need pressure modification for periodic BC in spanwise direction. Can you say how we implement the pressure periodic BC in spanwise direction?