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Riemann Problem Resolution and Godunov Scheme for the Aw-Rascle-Zhang Model

Author

Listed:
  • Salim Mammar

    (Technical Department for Transport, Roads and Bridges (SETRA), F-92220 Bagneux, Cedex, France)

  • Jean-Patrick Lebacque

    (INRETS/Gretia, “Les Descartes 2,” F-93166 Noisy le Grand, Cedex, France)

  • Habib Haj Salem

    (INRETS/Gretia, “Les Descartes 2,” F-93166 Noisy le Grand, Cedex, France)

Abstract

Recently, Aw and Rascle and Zhang introduced a new second-order macroscopic model, following the theoretical investigations on the Payne-Whitham second-order modelling by Daganzo. The conserved variables in this model are the density and the relative flow. The aim of this paper is to solve the Riemann problem for the Aw-Rascle-Zhang (ARZ) model for all possible initial conditions, using an extended fundamental diagram. The resolution of the Riemann problem provides the user of the model with a set of nontrivial analytical solutions; it is also a prerequisite for the construction of numerical solution schemes. Some examples are given in which analytical solutions of the Riemann problem are discussed and compared to numerical solutions. The ARZ model shows better fit to real data than the embedded Lighthill-Whitham-Richards (LWR) model for the same set of physical parameters.

Suggested Citation

  • Salim Mammar & Jean-Patrick Lebacque & Habib Haj Salem, 2009. "Riemann Problem Resolution and Godunov Scheme for the Aw-Rascle-Zhang Model," Transportation Science, INFORMS, vol. 43(4), pages 531-545, November.
    • Handle: RePEc:inm:ortrsc:v:43:y:2009:i:4:p:531-545
    DOI: 10.1287/trsc.1090.0283
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    References listed on IDEAS

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    1. Jiang, Rui & Wu, Qing-Song & Zhu, Zuo-Jin, 2002. "A new continuum model for traffic flow and numerical tests," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 405-419, June.
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    3. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    4. Daganzo, Carlos F., 1995. "Requiem for second-order fluid approximations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 277-286, August.
    5. Zhang, H. M., 2002. "A non-equilibrium traffic model devoid of gas-like behavior," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 275-290, March.
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    Cited by:

    1. Costeseque, Guillaume & Lebacque, Jean-Patrick, 2014. "A variational formulation for higher order macroscopic traffic flow models: Numerical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 112-133.
    2. Ranju Mohan & Gitakrishnan Ramadurai, 2015. "Submission to the DTA2012 Special Issue: A Case for Higher-Order Traffic Flow Models in DTA," Networks and Spatial Economics, Springer, vol. 15(3), pages 765-790, September.

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