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A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow. (English) Zbl 1292.90078
Summary: 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
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