When Does the Moment Basis Matter in Lattice Boltzmann Methods?

This arXiv preprint studies the theoretical role of the moment basis in central-moment lattice Boltzmann methods for fluid flow simulation. It shows that the basis enters the collision stage only through the conjugate of the relaxation matrix, and that two bases related by a constant matrix produce exactly the same scheme if and only if the corresponding commutator vanishes. The analysis therefore links the significance of orthogonalizing the basis to the geometry of the chosen velocity set, and examines the behavior restricted to physical states.