Construction and simulation of a novel continuous traffic flow model

In this paper, we aim to propose a novel mathematical model for traffic flow and apply a newly developed characteristic particle method to solve the associate governing equations. As compared with the existing non-equilibrium higher-order traffic flow models, the present one is put forward to satisfy the following three conditions: 1. Preserve the equilibrium state in the smooth region. 2. Yield an anisotropic propagation of traffic flow information. 3. Expressed with a conservation law form for traffic momentum. These conditions will ensure a more practical simulation in traffic flow physics: The current traffic will not be influenced by the condition in the behind and result in unambiguous condition across a traffic shock. Through analyses of characteristics, stability condition and steady-state solution adherent to the equation system, it is shown that the proposed model actually conform to these conditions. Furthermore, this model can be cast into its characteristic form which, incorporated with the Rankine-Hugoniot relation, is appropriate to be simulated by the characteristic particle method to obtain accurate computational results.