PHYSICAL SYMMETRY AND LATTICE SYMMETRY IN THE LATTICE BOLTZMANN METHOD

The lattice Boltzmann method (LBM) is regarded as a specific finite di fference discretization for the kinetic equation of the discrete veloc ity distribution function. We argue that for finite sets of discrete v elocity models, such as LBM, the physical symmetry is necessary for ob taining the correct macroscopic Navier-Stokes equations. In contrast, the lattice symmetry and the Lagrangian nature of the scheme, which is often used in the lattice gas automaton method and the existing latti ce Boltzmann methods and directly associated with the property of part icle dynamics, is not necessary for recovering the correct macroscopic dynamics. By relaxing the lattice symmetry constraint and introducing other numerical discretization, one can also obtain correct hydrodyna mics. In addition, numerical simulations for applications, such as non uniform meshes and thermo-hydrodynamics can be easily carried out and numerical stability can be ensured by the Courant-Friedricks-Lewey con dition and using the semi-implicit collision scheme.