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

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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.

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Received: 4 December 1997

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Helbing, D., Treiber, M. Enskog equations for traffic flow evaluated up to Navier-Stokes order. GM 1, 21–31 (1998). https://doi.org/10.1007/PL00010906

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Keywords

  • Traffic Flow
  • Congested Traffic
  • Space Requirement
  • Granular Flow
  • Linear Instability