Mathematics > Numerical Analysis
arXiv:2401.11787 (math)
[Submitted on 22 Jan 2024]
Title:A Comparative Study of Numerical Methods for Approximating the Solutions of a Macroscopic Automated-Vehicle Traffic Flow Model
View a PDF of the paper titled A Comparative Study of Numerical Methods for Approximating the Solutions of a Macroscopic Automated-Vehicle Traffic Flow Model, by George Titakis and 4 other authors
View PDFAbstract: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.
| Comments: | 34 pages, 19 figures |
| Subjects: | Numerical Analysis (math.NA) |
| Cite as: | arXiv:2401.11787 [math.NA] |
| (orarXiv:2401.11787v1 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2401.11787 arXiv-issued DOI via DataCite |
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View a PDF of the paper titled A Comparative Study of Numerical Methods for Approximating the Solutions of a Macroscopic Automated-Vehicle Traffic Flow Model, by George Titakis and 4 other authors
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