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Two algorithms for a fully coupled and consistently macroscopic PDE-ODE system modeling a moving bottleneck on a road

1 Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Via deiTaurini 19, 00185 - Rome, Italy
2 Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studidell’Aquila, Via Vetoio, 67100 - Coppito (AQ), Italy
3 Department of Mathematical Sciences, Rutgers University, 311 N 5th Street, Camden, NJ 08102,USA

In this paper we propose two numerical algorithms to solve a coupled PDE-ODE systemwhich models a slow vehicle (bottleneck) moving on a road together with other cars. The resulting system is fully coupled because the dynamics of the slow vehicle depends on the density of cars and, at the same time, it causes a capacity drop in the road, thus limiting the car flux. The first algorithm, based on the Wave Front Tracking method, is suitable for theoretical investigations and convergence results. The second one, based on the Godunov scheme, is used for numerical simulations. The case of multiple bottlenecks is also investigated.
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