Journal
KINETIC AND RELATED MODELS
Volume 13, Issue 2, Pages 279-307Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/krm.2020010
Keywords
Vehicular traffic; BGK models; Chapman-Enskog expansion; multiscale models; kinetic equations
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Funding
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy [EXC-2023, 390621612]
- DFG [HE5386/13-15]
- National Group for Scientific Computation (GNCS-INDAM)
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We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by deriving a modified formulation of the BGK-type equation. The new kinetic model allows to reproduce conditionally stable non-equilibrium phenomena in traffic flow. In particular, stop and go waves appear as bounded backward propagating signals occurring in bounded regimes of the density where the model is unstable. The BGK-type model introduced here also offers the mesoscopic description between the microscopic follow-the-leader model and the macroscopic Aw-Rascle and Zhang model.
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