A Comparative Study of Numerical Methods for Approximating the Solutions of a Macroscopic Automated-Vehicle Traffic Flow Model
CoRR(2024)
摘要
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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