Admissibility of a wide cluster solution in "anisotropic" higher-order traffic flow models

We analytically investigate a wide cluster solution and show that it is not admitted in some of the traffic flow models in the literature. For those traffic flow models that admit the wide cluster solution, the relationship between two important control parameters and the critical densities that divide an equilibrium solution into stable and unstable regions is thoroughly discussed in detail. We find that such wide clusters exist with a free traffic density in an unstable region, and with one or three critical densities. These results are different from the cases in the well-known higher-order traffic flow models of Payne and Whitham [H. J. Payne, "Models of freeway traffic and control," in Mathematical Models of Public Systems, A. G. Bekey, ed., Simulation Council Proc. Ser. 1, La Jolla, CA, 1971, pp. 51-61], [G. B. Whitham, Linear and Nonlinear Waves, John Wiley and Sons, New York, 1974], Kühne [R. D. Kühne, "Macroscopic freeway model for dense traffic-stop-start waves and incident detection," in Proceedings of the 9th International Symposium on Transportation and Traffic Theory, J. Volmuller and R. Hamerslag, eds., VNU Science Press, Utrecht, 1984, pp. 21-42], and Kerner and Konhäuser [B. S. Kerner and P. Konhäuser, Phys. Rev. E (3), 50 (1994), pp. 54-83]. © 2007 Society for Industrial and Applied Mathematics.published_or_final_versio

High-resolution central-upwind scheme for second-order macroscopic traffic flow models

Traffic flow models are important tools for traffic management applications such as traffic incident detection and traffic control. In this paper, we propose a novel numerical approximation method for second-order macroscopic traffic flow models. The method is based on the semi-discrete central-upwind numerical flux and high-order reconstructions for spatial discretizations. We then apply the designed high-resolution schemes to three representative types of second-order traffic flow models and perform a variety of numerical experiments to validate the proposed methods. The simulation results illustrate the effectiveness, simplicity and universality of the central-upwind scheme as numerical approximation method for macroscopic traffic flow models

Discontinuous Galerkin finite element scheme for a conserved higher-order traffic flow model by exploring Riemann solvers

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