Bounce-Back corner node

Lattice Boltzmann Method LBM: Theory
#1

Hi,
I just started LBM, I have a few questions about the bounce-back boundary conditions:

For example,
the D2Q9 lattice is like this:

7 3 6
4 1 2
8 5 9

Let’s assume node 1 is on the left-top corner, and node 2 is on the top boundary.

For node 2, after streaming, f1,f2,f4, f3,f7,f6 are known, only f8,f5,f9 are unknown, so we can apply the bounce back rules to calculate f8,f5,f9 like:
f8=f6; f5=f3; f9=f7;

But for node 1, I THINK after streaming, we only know f3, f4,f7, because those distribution functions are coming from the neighborhood nodes, but how can I get f6, f8, f2, f5, f9? if I apply bounce back rules, I might have:
f5=f3;f9=f7;f2=f4; how about f8 and f6?

Thanks!!

#2

What you will do with the unknown distribution functions will depend on what boundary conditions you want to impose on the left side.
For instance if you have periodic left-right, then you stream f6 from the right boundary of the domain.
If you have a wall on the left, you will want to bounce back f6 as well.
By the way, if you are using full way bounce-back, then most distributions only serve as a “temporary storage place”, and only f9 actually needs to be defined on your corner node, as the other distribution functions never go into the domain.

Nic