LBM is said to be of second order accuracy in space and time. Can we increase the temporal and spatial accuracy if we discretised the advection term of LBM with high order discretisation techniques (ex; third order upwind scheme, etc)??
of course you can increase the accuracy of the scheme. But in my opinion it will not be “lattice Boltzmann” anymore. It will be a higher order discretization of the continuous Boltzmann equation. There are some paper dedicated to this kind of methods. I put here one using spectral elements method