Realization of isotropy of the lattice Boltzmann method via rotation of lattice velocity bases

We present a detailed algorithm of rotationally invariant lattice Boltzmann method (RILBM). The suggested approach overcomes discrete artifacts present in the standard lattice Bhatnagar, Gross, and Krook (LBGK) model by introducing a generalized particle collision operator in arbitrarily rotated frames. We demonstrate that the Navier–Stokes equations are exactly recovered through the Chapman–Enskog expansion, and present two computational cases that show independence of numerical results relative to the lattice orientation.