Note on Invariance of One-Dimensional Lattice-Boltzmann Equation

Invariance of the one-dimensional lattice Boltzmann model is proposed together with its rigorous theoretical background. It is demonstrated that the symmetry inherent in Navier--Stokes equations is not really recovered in the one-dimensional lattice Boltzmann equation (LBE), especially for shock calculation. Symmetry breaking may be the inherent cause for the non-physical oscillations in the vicinity of the shock for LBE calculation.