Gas-kinetic derivation of Navier-Stokes-like traffic equations.

@article{Helbing1996GaskineticDO,
  title={Gas-kinetic derivation of Navier-Stokes-like traffic equations.},
  author={Helbing},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={1996},
  volume={53 3},
  pages={
          2366-2381
        }
}
  • Helbing
  • Published 1 March 1996
  • Computer Science
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
Macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies. Therefore, this paper shows how to construct a logically consistent fluid-dynamic traffic model from basic laws for the acceleration and interaction of vehicles. These considerations lead to the gas-kinetic traffic equation of Paveri-Fontana. Its stationary and spatially homogeneous solution implies equilibrium relations for the `fundamental diagram', the… 
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