Granular Matter

, Volume 1, Issue 1, pp 21–31 | Cite as

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

  • Dirk Helbing
  • Martin Treiber

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations