# fully developed boundary condition

Hi dear freinds!
how can I implement fully developed BC for outlet flow in the channel? I know U(Nx,y)=U(Nx-1,Y) in this simulatin. How can I relate this condition to distribution function f? I want to have a relation o equation to find unkown f3,F6,F7 in outlet?

Hello,

actually you impose u(nx,y)=u(nx-1,y) and then use this condition as Dirichlet BC. For more details see [lbmethod.org].

Orestis

Hi,
you can apply first order finite difference discritization of df/dx=0 for three directions f3,f6, and f7 as below:
consider three nodes i-2,i-1,i in the way that node i places exactly on the outlet boundary and i-1,i-2 are two nodes before outlet boundary , then disceretize df/dx=0 for example in direction related to f3

f_3(i-2)-f_3(i-1)=f_3(i-1)-f_3(i) then f_3(i)=2*f_3(i-1)-f_3(i-2)
do the same for other two directions f6,f7

good luck

Hi r.imani,

I am simulating flow in a chamber. i am using Guo’s non-equilibrium extrapolation scheme. I know inlet velocity and at outlet pressure is 1 atm.my Re=200.I have written my inlet BC as
rho[NY-1][i] = rho[NY-2][i];
u_x[NY-1][i] = 0.0;
u_y[NY-1][i] = U = 0.05;
and out flow BC as follows.
rho[NY-1][i] = rho[NY-2][i];
u_x[NY-1][i] = u_x[NY-2][i];
u_y[NY-1][i] = u_y[NY-2][i];
My density is decreasing for every iteration. what went wrong with my code?. i have doubt regarding implementation of BC.