Dear all,

I am facing some difficulties implementing a simple Couette flow!

In my case, however, instead of using periodic BCs at inlet/outlet, as usual, I intend to use velocity BC there. As a result, the domain has 4 velocity BCs at the 4 boundaries.

For that I am using Zou He BC.

Since the LB solution must be equal to the analytical one. This problem allows me to benchmark my velocity BCs implementation.

The problem is that I do not obtain the aimed exact solutions and as far as I understand the problem comes from the corners.

When the wall velocity is zero the corner implementation is that given in Zou He paper. However in the case the wall is moving the non-equilibrium bounce-back condition is not equivalent to the straight bounce-back formula.

Yet I thought the required modifications would be straightforward. For instance for the top-left corner:

```
x=1; y=LY;
u(x,y)=Umax;
v(x,y)=0;
rho(x,y)=rho(x,y-1);
f(x,y,1)=f(x,y,3)+2/3*rho0*u(x,y);
f(x,y,4)=f(x,y,2)-2/3*rho0*v(x,y);
f(x,y,8)=f(x,y,6)+1/6*rho0*(u(x,y)-v(x,y));
f(x,y,5)=1/2*(rho(x,y)-(f(x,y,9)+f(x,y,1)+f(x,y,2)+f(x,y,3)+f(x,y,4)...
+f(x,y,6)+f(x,y,8)));
f(x,y,7)=f(x,y,5)-1/6*rho0*(u(x,y)+v(x,y));
```

However, my reasoning appears to be wrong.

Does anyone have ever tried to do the same thing?

If so, could you please provide me some help/suggestion here. I would be much appreciated.

Thank you advance.

Goncalo