Derivation of the lattice vehicular model from the Boltzmann transport equation

Abstract:- In this paper, the lattice vehicular model, which is in the form the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. A 3-bit approximation, which describe uncongested traffic flow, for the discretization of the Boltzmann equation in both time and phase space is discussed in detail. The lattice vehicular Boltzmann model ensures vehicles would not travel backward. A general procedure to derive the vehicular lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly.