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Here is the flow past a square cylinder configuration. The problem is a viscous and incompressible with parabolic velocity profile using freestream velocity U across single cylinder. I use the single relaxation time lattice boltzmann method. For the two-dimensional nine-velocity lattice(D2Q9), the particles directions are shown in the picture.

enter image description here

The parameters: H=160, L=780, I=170, D=20, Umax=0.0438, density=1.0, dy=dx=1, dt=1,Re=160

The boundary conditions: Inlet: He-Zou boundary condition Wall: bounce-back conditions Outlet: interpolation(Here is the code for outlet BCs)

f(1,n,j)=2*f(1,n-1,j)-f(1,n-2,j)
f(5,n,j)=2*f(5,n-1,j)-f(5,n-2,j)
f(8,n,j)=2*f(8,n-1,j)-f(8,n-2,j)

My problem is that whether the outlet boundary conditions is right or not. If it is right, why it's about f1, f5, f8 rather than f3, f6, f7? In my opinion, it seems that we can't get f3, f6, f7 form streaming on the outlet.

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Your outlet boundary condition is not correct. In your outlet BCs, you have to impose the value of $f_6$, $f_3$ and $f_7$ since these populations are not updated by the streaming step.

This paper presents a good example on how to do an outflow BC in LBM : https://www.researchgate.net/publication/40536594_Outflow_boundary_conditions_for_the_lattice_Boltzmann_method

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