# Symmetry Boundary Condition

Hi All,

I’m looking for some information on how to define symmetry BC in LBM. Please, could anyone give me an advice?

Kind Regards,
Francois

I think Yu et al (Viscous flow computations with the method of lattice Boltzmann equation) have looked at this.

Hi,

I think I’ve seen a symmetry boundary condition given in an article somewhere (I don’t think it was the one Tim referred to), but I don’t remember which one. It might actually have been something about a full-slip boundary, as opposed to no-slip. I do think I remember the principle of the BC, though. Essentially, if you have particles streaming towards the symmetry BC, they will bounce off specularly, instead of being reflected right back as with the half-way no-slip bounce-back BC. This simulates particles being streamed from the other side of the symmetry BC. I’ll draw some examples to show the principle (but please forgive my poor ASCII art skills!).

In these drawings, the regular |s and -s indicate the border between two nodes, while lines inside these nodes indicate individual particle distributions. (You have to imagine them as part of the D2Q9 velocity vector figure that you can find in many, many LB articles.) The =s indicate the symmetry BC. First, an example of what happens to diagonal distributions hitting the BC:

``````
Before streaming
|---|---|
|   |   |
|   |   |
|  \|   |
=========

After streaming
|---|---|
|   |  /|
|   |   |
|   |   |
=========

``````

Then, what happens to particles hitting the BC head on:

``````
Before streaming
|---|---|
|   |   |
|   |   |
| | |   |
=========

After streaming
|---|---|
| | |   |
|   |   |
|   |   |
=========

``````

And I think that should be the gist of it. Of course, this BC only works if the line of symmetry lies along the axis of the grid of nodes…

Erlend