Granular Matter

, Volume 1, Issue 1, pp 21–31

Enskog equations for traffic flow evaluated up to Navier-Stokes order

  • Dirk Helbing
  • Martin Treiber

DOI: 10.1007/PL00010906

Cite this article as:
Helbing, D. & Treiber, M. GM (1998) 1: 21. doi:10.1007/PL00010906

Abstract

Similarly to the treatment of dense gases and granular flows, Enskog-like kinetic equations are formulated for the dynamics of unidirectional freeway traffic. From these we derive fluid-dynamic equations, which, in comparision with ordinary gases or fluids, contain additional terms due to the dissipative and anisotropic vehicle interactions. It is shown that velocity-dependent space requirements are needed for a realistic description of congested traffic situations and unstable traffic flow. Apart from a calculation of Euler order equations, we indicate how Navier-Stokes corrections could be obtained by means of the relaxation approximation. A linear instability analysis indicates that the Navier-Stokes equations show an additional instability, which is confirmed by simulations. Nevertheless, the Euler and Navier-Stokes equations give rise to similar stop-and-go waves in the non-linear regime. The relevance of the proposed methods and results for describing granular flows is outlined.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Dirk Helbing
    • 1
  • Martin Treiber
    • 1
  1. 1.II. Institute for Theoretical Physics, University of Stuttgart, Pfaffen waldring 57, D-70550 Stuttgart, Germany e-mail: helbing@theoz.physik.uni-stuttgart.de DE

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