Halfway bounceback

Lattice Boltzmann Method LBM: Algorithms
#1

Hello everyone,
I need a simple code (Poiseuil 2D) with the boundary conditions Halfway. I was able to implement (Poiseuil 2D, 3D) with the boundary condition Fullway, but for the boundary conditions Halfway I still have a problem. I count on your kindness. Thank you in Avence.

#2

Hi zarbaya,

Have you had a look at the following post?
http://www.palabos.org/forum/read.php?9,7184

The half-way boundary is explained in simple terms.
If you want, you can post your code with full-way bounce-back and we’ll see how to change it for half-way.

Regards,
ndel

#3

Hello nicolasD and everyone in this forum :slight_smile:

I’m struggling with the exact same problem right now, but somehow the velocities on the solid nodes won’t be negative.
The only thing I get is zero velocity in flow direction on the walls just like in a fullway bounceback. Can you please help me turn this to a halfway bounceback?

I also wonder if my body force implementation is correct.

Thanks in advance,
Totomo

P.s.: Here’s an extract from my MATLAB code:


% define matrices and variables
...


% initialization

for a = 1 : 9
    
    uc = (cx(a)*ux(1) + cy(a)*uy(1));
    
    f_prop(:,:,a) = rho * w(a) * ( 1 + uc/cs^2 + uc.^2/(2*cs^4) - (ux.^2+uy.^2)/(2*cs^2) );
    
end


for t = 1 : runtime
    
    % adding body force

    ux = ux + dt * Fx ./ (2*density);
    uy = uy + dt * Fy ./ (2*density);
    
    % calculate equilibrium
    
    for a = 1 : 9
        
        uc = ( cx(a)*ux(:,:) + cy(a)*uy(:,:) );
        
        f_eq(:,:,a) = rho * w(a) * ( 1 + uc/cs^2 + uc.^2/(2*cs^4) - (ux(:,:).^2+uy(:,:).^2)/(2*cs^2) );
        
    end
    
    
    % collision with body force
    
    for i = 1 : ly
        for j = 1 : lx
            for a = 1 : 9
                
                F_a(i,j,a) = (1 - 1/(2*tau)) * w(a) * ( ( (c(1,a) - ux(i,j)) / cs^2 + ...
                    (c(1,a) * ux(i,j) + c(2,a) * uy(i,j)) * c(1,a) / cs^4 ) * Fx + ...
                    ( (c(2,a) - uy(i,j)) / cs^2 + (c(1,a) * ux(i,j) + c(2,a) * uy(i,j)) * ...
                    c(2,a) / cs^4 ) * Fy );
                
            end
        end
    end
    
    for a = 1 : 9
        
        f_c(:,:,a) = f_prop(:,:,a) - 1/tau * (f_prop(:,:,a) - f_eq(:,:,a)) + dt * F_a(a);
        
    end
    

    % bounceback
    
    for g = 1 : length(row)
        
        temp = f_c(row(g),col(g),7); f_prop(row(g),col(g),7) = f_c(row(g),col(g),5); f_prop(row(g),col(g),5) = temp;
        temp = f_c(row(g),col(g),4); f_prop(row(g),col(g),4) = f_c(row(g),col(g),2); f_prop(row(g),col(g),2) = temp;
        temp = f_c(row(g),col(g),8); f_prop(row(g),col(g),8) = f_c(row(g),col(g),6); f_prop(row(g),col(g),6) = temp;
              
    end


    % propagation / streaming
    
    for i = 1 : ly
        
        if i > 1
            in = i-1;
        else
            in = ly;
        end
        
        if i < ly
            ip = i+1;
        else
            ip = 1;
        end
        
        for j = 1 : lx
            
            if j > 1
                jn = j-1;
            else
                jn = lx;
            end
            if j < lx
                jp = j+1;
            else
                jp = 1;
            end
            
            ftemp(i,j,9)  = f_c(i,j,9);
            ftemp(i,jp,1) = f_c(i,j,1);
            ftemp(ip,j,4) = f_c(i,j,4);
            ftemp(i,jn,3) = f_c(i,j,3);
            ftemp(in,j ,2) = f_c(i,j,2);
            ftemp(ip,jp,8) = f_c(i,j,8);
            ftemp(ip,jn,7) = f_c(i,j,7);
            ftemp(in,jn,6) = f_c(i,j,6);
            ftemp(in,jp,5) = f_c(i,j,5);
            
        end
    end
    
    f_prop(:,:,:)=ftemp(:,:,:);
    

    % density and velocity
    
    density = sum(f_prop,3);
    
    ux = (f_prop(:,:,1)-f_prop(:,:,3)+f_prop(:,:,5)-f_prop(:,:,6)+f_prop(:,:,8)-f_prop(:,:,7))./density;
    uy = (f_prop(:,:,2)-f_prop(:,:,4)+f_prop(:,:,5)-f_prop(:,:,8)+f_prop(:,:,6)-f_prop(:,:,7))./density;
    

    % visualization
    ...
#4

Hi Zahrbaya,

could you share it with us your code?

thank you