Thanks a lot Jlatt,
I couldn’t get that review paper!
I switched back to a 2D case to make it easier!
I followed the following paper
Yonghao Zhang, Rongshan Qin, David R Emerson, “Lattice Boltzmann simulation of rarefied gas flows in microchannels”, Physics Review E71 047702 (2005)
The equations (7) in the paper are for collision part on the wall.
To calculate BC on the wall for example upper wall I used bounce back to derive equations for unknown directions!
Sigma(f) = Rho
Sigma (fi * ey(i)) = Rho * V =0
Sigma (fi * ex(i) = Rho * U slip
At the end of every time step the Uslip was calculated to get used for the next time step.
J = NY
Do = 1, NX
Rho(I,J) = f(I,J,1)+f(I,J,3)+f(I,J,9)+2.0* (f(I,J,2)+f(I,J,5)+f(I,J,6))
f(I,J,4) = f(I,J,2)
f(I,J,7) = (f(I,J,1)-f(I,J,3)+2.d0*f(I,J,5)- Rho(I,J)*Uslip)/2.d0
f(I,J,8) = f(I,J,5)+f(I,J,6)-f(I,J,7)
I assumed Uslip of every grid point constant for every time step.
I calculated Uslip based on equation (8) in the paper.
Please let me know if what I did is right! Can I use bounce back to calculate BC for a slip flow BC case?
I couldn’t get good result!
All the best,