  A lattice Boltzmann (LB) theory, analytical characteristic integral (ACI) LB
theory, is proposed in this paper. ACI LB theory takes Bhatnagar-Gross-Krook
(BGK) Boltzmann equation as the exact kinetic equation behind Navier-Stokes
continuum and momentum equations and constructs LB equation by rigorously
integrating BGK-Boltzmann equation along characteristics. It's a general
theory, supporting most existed LB equations including the standard lattice BGK
(LBGK) equation inherited from lattice-gas automata, whose theoretical
foundation had been questioned. ACI LB theory also indicates that the
characteristic parameter of LB equation is collision number, depicting the
particle-interacting intensity in the time span of LB equation, instead of
traditionally assumed relaxation time, and the over relaxation time problem is
merely a manifestation of temporal evolution of equilibrium distribution along
characteristics under high collision number, irrelevant to particle kinetics.
In ACI LB theory, the temporal evolution of equilibrium distribution along
characteristics is the determinant of LB method accuracy and we numerically
prove it.
