I am about to start developing a 2D LBM foe shallow water modelling using D2Q5 scheme; there are plenty of D2Q9 schemes out there but I didn’t come across any D2Q5, except those for advection-diffusion modelling. However, I have been reading several literature saying that D2Q5 cannot be used for “fluid flow” modelling as it does not meet symmetry requirements needed for the non-linear Navier-Stokes equation. I am not quite sure why? There are plenty of 1D LBMs out there used for shallow water modelling so how is that a 5-point lattice (D2Q5) cannot do what a 3-point (D1Q3) can do???