No-Slip Boundary Conditions

Lattice Boltzmann Method LBM: Theory
#1

Hi All,

Can I modify the Zou-He boundary conditions for velocity and use them for No-Slip? I do the collision on all the nodes in the domain.

My code goes as follows.


              % Zou-He No-Slip Boundary
                if y==1
                    
                    f(x,y,2) = f(x,y,4);
                    f(x,y,5) = f(x,y,7) - 0.5*(f(x,y,1) - f(x,y,3));
                    f(x,y,6) = f(x,y,8) + 0.5*(f(x,y,1) - f(x,y,3));
                    
                elseif y==YMAX
                    
                    f(x,y,4) = f(x,y,2);
                    f(x,y,7) = f(x,y,5) + 0.5*(f(x,y,1) - f(x,y,3));
                    f(x,y,8) = f(x,y,6) - 0.5*(f(x,y,1) - f(x,y,3));
                    
                end

I got these equations by substituting the velocity terms to zero. When I try to simulate the poiseulle flow, I get zero velocity on the boundary (wall) nodes.

Thanks,
Narender

#2

Dear Narender,

You can certainly use them for no-slip conditions. Authors in their article checked it as well.

Cheers,
Alex

#3

Dear Alex,

Thanks for the reply. I guess this is the easiest way to get the no-slip on the exact boundary. I mean, we need not use a extra node to account for the assumption that the boundary is half way between the last node and pre-last node.

Please correct me if I am wrong.

Thanks,
Narender

#4

Dear Narender,

You are right. In this case the boundary is located exactly at the node. However, one should be cautious to use Zou-He boundary conditions because sometimes they produce mass increase in the domain, which is OK as far as all physical quantities are right.

Cheers,
Alex