A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow.

*(English)*Zbl 1292.90078Summary: We introduce a numerical method for tracking a bus trajectory on a road network. The mathematical model taken into consideration is a strongly coupled PDE-ODE system: the PDE is a scalar hyperbolic conservation law describing the traffic flow while the ODE, that describes the bus trajectory, needs to be intended in a Carathéodory sense. The moving constraint is given by an inequality on the flux which accounts for the bottleneck created by the bus on the road. The finite volume algorithm uses a locally non-uniform moving mesh which tracks the bus position. Some numerical tests are shown to describe the behavior of the solution.

##### MSC:

90B20 | Traffic problems in operations research |

65K05 | Numerical mathematical programming methods |

35L65 | Hyperbolic conservation laws |

65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |

##### Keywords:

conservation laws with constraints; traffic flow modeling; PDE-ODE model; numerical simulations; front-tracking methods
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\textit{M. L. Delle Monache} and \textit{P. Goatin}, Discrete Contin. Dyn. Syst., Ser. S 7, No. 3, 435--447 (2014; Zbl 1292.90078)

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