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

TL;DR

This paper introduces two numerical algorithms for a coupled PDE-ODE system modeling a moving bottleneck on a road, capturing the interaction between a slow vehicle and traffic density, with theoretical and numerical analysis.

Contribution

It presents a wave front tracking-based algorithm for theoretical analysis and a Godunov scheme for numerical simulations of a coupled PDE-ODE traffic model.

Findings

Wave front tracking algorithm suitable for convergence analysis

Godunov scheme effective for simulations

Extension to multiple bottlenecks explored

Abstract

In this paper we propose two numerical algorithms to solve a coupled PDE-ODE system which 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.