Hi All, I am working on flow over a cylinder. When I use the NBC mentioned in the document “How to impose a Neumann boundary condition with the lattice Boltzmann method” by Orestis I get a strong reflection from the outlet and my result blows up. The code is as follows. Please let me know what mistake I am doing.

```
!Outflow condition
!Macroscopic NBC
u(x,y,0) = (4.0*u(x-2,y,0) - u(x-1,y,0))/3.0; ! x velocity extrapolation
u(x,y,1) = (4.0*u(x-2,y,1) - u(x-1,y,1))/3.0; ! y velocity extrapolation
! Microscopic Zou-He
rho(x,y) = -rho0*u(x,y,0) + (f(x,y,0) + f(x,y,2) + f(x,y,4)) + 2.0*(f(x,y,5)+f(x,y,1)+f(x,y,8));
f(x,y,3) = f(x,y,1) - (2.0/3.0)*rho0*u(x,y,0);
f(x,y,7) = f(x,y,5)-(1.0/6.0)*rho0*u(x,y,0)-(1.0/2.0)*rho0*u(x,y,1)+(1.0/2.0)*(f(x,y,2)-f(x,y,4));
f(x,y,6) = f(x,y,8)-(1.0/6.0)*rho0*u(x,y,0)+(1.0/2.0)*rho0*u(x,y,1)+(1.0/2.0)*(f(x,y,4)-f(x,y,2));
```

My flow parameters are as follows

```
xDim = 1200
yDim = 165
obstX = 81 ! grid points
obstY = 81 ! grid points
obstR = 20 ! lattice units
Re = 100
u_in = 0.066666 ! average inlet velocity
nu = 2.0*obstR*u_in/Re = 0.026666664
tau = (6.0*nu+1.0)/2.0 = 0.58
```

Thanks in advance.