First note that LBM doesn't actually work for in-compressible fluids unless you replace the density in your D2Q5 vectors with pressure (or energy etc.. something that doesn't relate to the number of particles per unit volume/area), as density is constant in in-compressible fluids (and I'll be from this point onward considering your LBM implementation in terms of pressure, not density). Second I would probably need to see the code, but it appears your equilibrium equation is wrong.
It looks like your equilibrium equation results in collisions with little to no perpendicular flow, and hence why it just looks like a straight shot across your grid.
Here is visual explanation:
imagine the following adjacent grid points, where blue represents non zero pressure.
On the next step, this is what your simulation looks like it is doing:
This is what it should be doing:
Collisions should result in perpendicular pressure flow to some degree. Think of billiard balls, if you hit one to the side, the ball doesn't just go straight, it hits off at an angle. 568
Now you may be thinking "even with the billard ball situation, I can't get it to go exactly perpendicular to my collision!" and there are two factors to this:
* First LBM equilibrium collision equations happen at the particle level, and the equilibrium equation is supposed to not handle just one collision, but multiple collisions in a time-step. You in effect have multiple "billiard ball" collisions to account for (example):
* The quantized 4 directions + stationary (the Q5 in D2Q5) in LBM are not just supposed to be for the aligned particle movement to that quantized direction, but rather all particles angles more closely aligned with that angle than others. Here is what I'm talking about:
Each color should correspond to all particles flowing in that solid angle range, not just the particles that happen to flow aligned to the axis. Even in the single collision in the billard ball situation, the ball could still end up going in the "left general direction" despite not moving directly left, and would be advected leftwards.
I'm not sure what your equilibrium equation is, but I would suggest making it more isotropic, making sure that (if for example you use energy) you conserve energy. 621