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arXiv · 2401.11787

A Comparative Study of Numerical Methods for Approximating the Solutions of a Macroscopic Automated-Vehicle Traffic Flow Model

George Titakis·Iasson Karafyllis·Dionysis Theodosis·Ioannis Papamichail·Markos Papageorgiou
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Abstract

In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the macroscopic traffic model: mass is preserved, the mechanical energy is decaying and an energy functional is also decaying. To demonstrate the advantages of the particle method under consideration, a comparison with other numerical methods for viscous compressible fluid models is provided. Since the solutions of the macroscopic traffic model can be approximated by the solutions of a reduced model consisting of a single nonlinear heat-type partial differential equation, the numerical solutions produced by the particle method are also compared with the numerical solutions of the reduced model. Finally, a traffic simulation scenario and a comparison with the Aw-Rascle-Zhang (ARZ) model are provided, illustrating the advantages of the use of automated vehicles.

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George Titakis, Iasson Karafyllis, Dionysis Theodosis, Ioannis Papamichail, Markos Papageorgiou. 2024-01-22. A Comparative Study of Numerical Methods for Approximating the Solutions of a Macroscopic Automated-Vehicle Traffic Flow Model. https://arxiv.org/abs/2401.11787

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