Slip Boundary Condition for Lid driven cavity flow

Lattice Boltzmann Method LBM: Theory
#1

Hi,
For Lid lidriven cavity flow with top wall moving i have assumed bounce back rule to all the walls except the top wall.

I’ve have been using velocity boundary by Zou & He which asssumes bounce back rule is true. Is this correct or I should use slip bounday condition.

If so can you please recommend me how to implement the slip boundary condition with a sample code.

It will be really helpful for me.

Thanks in advance.

#2

By the ‘slip’ boundary, do you actually just mean the moving wall? The moving wall in normal lid driven cavity flow still has a no slip condition - the fluid moves with the same velocity as the wall. Actually slip is a lot more difficult.

If no-slip is indeed what you mean then Zou and He for the moving wall should work reasonably well. Another option is to set the incoming f_i at the moving wall to be their equilibrium value (f_i=feq_i) and using the wall velocity and density in the equilibrium. This turns out to be the same a diffuse-refection, I think. I’m not sure which, if either, is better.

The things to be careful of are:

  1. bounce back places the wall roughly half way between grid points but Zou and He places a wall precisely on grid points
  2. corners can be difficult
  3. there is a numerical slip error due to bounce back, but this is small for large Reynolds numbers
  4. BGK simulations for 2D flows with no-slip (non-moving) boundary conditions are unstable for anything other than bounce back, as far as I’m aware anyway. In other words, if you used Zou and He on all the walls then you’d find it hard to reach Reynolds numbers over 1000 on reasonably sized grids (the benchmark tests use a 257*257 grid)