# Slip flow boundary condition for a 3D case

Dear friends,

I am working on 3D thermal LBM and I am going to simulate heat transfer and flow in a rectangular microchannel. I need to have slip flow boundary condition in my simulation. Dose anybody know a good paper that help me implement this boundary condition?

Any help is appreciated.
Mahshid

This is not an answer but a follow up question. That is, if OpenLB has any implementation of slip boundary condition

@Mashid: this depends on the type of thermal LB model you are using.
@Chuckdee: yes, there is. In the case of xFlows, boundary conditions are fully documented in the user’s guide.

Thanks Jlatt,

I used the following paper to develop my thermal code:

Y. Peng, C. Shu, Y.T. Chew
A 3D incompressible thermal lattice Boltzmann model and its application to simulate natural convection in a cubic cavity,
Journal of Computational Physics 193 (2003) 260–274

I couldn’t find a good paper about 3D thermal with slip flow BC.
If you know any good paper even with a different thermal model or any help please let me know! I need to know how I should calculate Kn number.

OK, as far as I could see, the thermal model in this paper is based on the Boussinesq approximation: the fluid is simulated with a normal Navier-Stokes solver, including an external force term for buoyancy effects. The temperature is simulated separately with an advection-diffusion equation.

For the fluid, you can then use the same boundary conditions as for non-thermal models. See for example the boundary conditions listed in this review paper.

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)
``````

## End Do

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,
Mahshid