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In this paper we propose two numerical algorithms to solve a coupled PDE-ODEsystem which models a slow vehicle (bottleneck) moving on a road together withother cars. The resulting system is fully coupled because the dynamics of theslow vehicle depends on the density of cars and, at the same time, it causes acapacity drop in the road, thus limiting the car flux. The first algorithm,based on the Wave Front Tracking method, is suitable for theoreticalinvestigations and convergence results. The second one, based on the Godunovscheme, is used for numerical simulations. The case of multiple bottlenecks isalso investigated.

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