2D D2Q9 lattice Boltzmann simulation of flow over a flat plate

Hi all,

I am currently attempting to model 2D incompressible flow over a flat plate using the standard D2Q9 lattice Boltzmann method. I am comparing my results with the Blasius solution i.e. the similarity variable (eta) vs. the non-dimensionalised u and v velocity components at various positions along the plate. I am getting errors of approximately 50% when compared to the Blasius solution.

I was just wondering if anybody had any tips on why this might be happening? I have set up the problem as follows:

  1. The plate is situated at bottom of the domain with a small section of open flow before the plate. I am simulating the section before the plate using half-way free-slip or symmetrical boundary conditions. I am using half-way bounceback boundary conditions to simulate no-slip conditions for the plate.

  2. I have a constant u velocity at the inlet and I am using the equilibrium scheme to simulate this (constant density of 1 and v velocity set to 0).

  3. The equilibrium scheme is also used at the top of the domain using the same parameters as the inlet. The top of the domain is situated far above the maximum boundary layer thickness so that the boundary conditions do not cause any unphysical effects.

  4. Zero gradient conditions are used for the outlet.

Is there anything that I am doing that immediately seems incorrect? I would sincerely appreciate any help with this. I am currently implementing a GPU code to drastically increase the mesh density and determine whether this improves accuracy (my current meshes are in the order of 100 x 1000, 200 x 2000 etc. in x and y respectively), but I just wanted to check if my overall approach to the problem is correct as well.

Thanks in advance,