I've implemented 2-dimensional, incompressible, high-reynolds fluid-flow using the Lattice Boltzmann Method on a D2Q9 lattice. My main goal is just visual plausibility, not quantitative accuracy. The simulation is initialised in equilibrium and in a small portion of space in the center a constant force to the right is exerted onto the fluid (to simulate a small "pump" to test the flow). The flow nicely moves rightward with emerging vorticies at the top and bottom of the flow as well as turbulence due to shear forces, as expected.
In order to speed up the simulation I experimented with using a D2Q5 lattice instead, but visual plausibility breaks down as no vorticies or any sort of turbulence emerges, just a boring narrow laminar flow to the right. I'd assume the reason is that in D2Q9 shear forces are considered due to the exchange with diagonally neighboring cells which are missing in D2Q5. Therefore the latter does not capture shear forces which are essential for turbulence, vorticies and so on. Since D2Q5 seems to be a practical choice in a bunch of papers I strongly assume I'm missing something here, as completely neglecting shear forces can not result in a physically sound (and not even visually pleasing) flow. See here for comparison:
Can somebody explain to me how D2Q5 is supposed to capture shear forces ? I really don't understand it conceptually.