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The vanishing pressure limits of Riemann solutions for the Aw-Rascle hydrodynamic traffic flow model with the logarithmic equation of state

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  • Xin, Xueli
  • Sun, Meina

Abstract

Two kinds of Riemann solutions for the Aw-Rascle hydrodynamic traffic flow model with the logarithmic equation of state are explicitly obtained by using the combination between 1-rarefaction or 1-shock wave along with 2-contact discontinuity. The formation of vacuum state and delta shock wave is identified and analyzed when the perturbation parameter in the pressure term drops to zero, where the intrinsic cavitation and concentration phenomena are surveyed and explored concretely. Additionally, several numerical results displaying the formation process of vacuum state and delta shock wave are also presented by taking three different perturbation parameters for comparison.

Suggested Citation

  • Xin, Xueli & Sun, Meina, 2024. "The vanishing pressure limits of Riemann solutions for the Aw-Rascle hydrodynamic traffic flow model with the logarithmic equation of state," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924002236
    DOI: 10.1016/j.chaos.2024.114671
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    References listed on IDEAS

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    1. Shagolshem, Sumanta & Bira, B. & Sil, Subhankar, 2022. "Conservation laws and some new exact solutions for traffic flow model via symmetry analysis," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    2. Chhatria, Balakrishna & Raja Sekhar, T. & Zeidan, Dia, 2024. "Limiting behaviour of the Riemann solution to a macroscopic production model with van der Waals equation of state," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    3. Borsche, Raul & Klar, Axel & Zanella, Mattia, 2022. "Kinetic-controlled hydrodynamics for multilane traffic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    4. 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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