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Two algorithms for a fully coupled and consistently macroscopic PDE-ODEsystem 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, Universit`a 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 resultingsystem 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 convergenceresults. The second one, based on the Godunov scheme, is used for numerical simulations. The caseof multiple bottlenecks is also investigated.
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Keywords conservation laws; discontinuous ODEs; fluid dynamic models; LWR model

Citation: Gabriella Bretti, Emiliano Cristiani, Corrado Lattanzio, Amelio Maurizi, Benedetto Piccoli. Two algorithms for a fully coupled and consistently macroscopic PDE-ODEsystem modeling a moving bottleneck on a road. Mathematics in Engineering, 2018, 1(1): 55-83. doi: 10.3934/Mine.2018.1.55

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