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The NHRS scheme for the two models of traffic flow

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Abstract

Within the numerical framework of non-homogeneous Riemann solver (NHRS) the nonlinear models characterizing traffic flows are investigated. Namely, we investigate the Lighthill–Whitham–Richards (LWR) traffic flow model and the Aw–Rascle model with a two-parameter flux approximation containing pressure. One of the main merits of this scheme, it computes the numerical flux corresponding the real state of solution in the obscurity of Riemann solution. Applying our scheme to a wide variety of numerical test cases, shows the high resolution of the proposed technique. Indeed, the presented results emphasizes the capability of this scheme to eliminate the oscillations of the classical schemes and controlling numerical diffusion. Numerical solutions are compared with Rusanov scheme, modified Lax–Friedrichs and the analytical solution. The presented results illustrate the precise resolution of the NHRS scheme. Indeed, the solutions of the NHRS scheme is more accurate than the solutions of the modified Lax–Friedrichs, Rusanov scheme. Finally, the proposed scheme is such a strong tool to tackle numerous different models in real-life problems.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Kamel Mohamed & Mahmoud A. E. Abdelrahman

  2. Department of Mathematics, Faculty of Science, New Valley University, New Valley, Egypt

    Kamel Mohamed

  3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Mahmoud A. E. Abdelrahman

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  1. Kamel Mohamed
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  2. Mahmoud A. E. Abdelrahman
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Correspondence to Mahmoud A. E. Abdelrahman.

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Communicated by Corina Giurgea.

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Mohamed, K., Abdelrahman, M.A.E. The NHRS scheme for the two models of traffic flow. Comp. Appl. Math. 42, 53 (2023). https://doi.org/10.1007/s40314-022-02172-y

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