A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow

Maria Laura Delle Monache; Paola Goatin

doi:10.3934/dcdss.2014.7.435

Article Contents

2014, Volume 7, Issue 3: 435-447. Doi: 10.3934/dcdss.2014.7.435

This issue Previous Article Discussion about traffic junction modelling: Conservation laws VS Hamilton-Jacobi equations Next Article Fundamental diagrams for kinetic equations of traffic flow

A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow

Maria Laura Delle Monache^1, and
Paola Goatin^2,

1.
Inria Sophia Antipolis-Méditerranée - EPI OPALE, 2004, Route des Lucioles - BP 93, 06902 - Sophia Antipolis Cedex
2.
INRIA Sophia Antipolis - Méditerranée, EPI OPALE, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex

Received: June 30, 2013

Revised: July 31, 2013

Published: May 2014

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Abstract

In this paper 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.

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Mathematics Subject Classification: Primary: 58J45, 35L65; Secondary: 90B20.

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