The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system.The analysis identifies the types and stabilities of the equilibrium solutions,and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison.The analytical and numerical results are in agreement,and may help to explain the simulated phenomena,such as the stop-and-go wave and oscillation near a bottleneck.The findings demonstrate the model ability to describe the complexity of congested traffic.
A standard conservation form is derived in this paper.The hyperbolicity of Helbing's fluid dynamic traffic flow model is proved,which is essential to the general analytical and numerical study of this model.On the basis of this conservation form,a local discontinuous Galerkin scheme is designed to solve the resulting system efficiently.The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is simulated.This simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients,and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.
