Numerical approximations of a traffic flow model on networks

Gabriella Bretti; Roberto Natalini; Benedetto Piccoli

doi:10.3934/nhm.2006.1.57

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2006, Volume 1, Issue 1: 57-84. Doi: 10.3934/nhm.2006.1.57

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Numerical approximations of a traffic flow model on networks

1.
Department of Engineering of Information and Applied Mathematics, DIIMA, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA)
2.
Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico, 137, 00161, Roma
3.
Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico 137, 00161 Roma

Received: August 31, 2005

Revised: September 30, 2005

Published: February 2006

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Abstract

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are considered as graphs composed by arcs that meet at some junctions. The crucial point is represented by junctions, where interactions occur and the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative methods, such as the classical Godunov scheme and the more recent discrete velocities kinetic schemes with the use of suitable boundary conditions at junctions. Riemann problems are solved by means of a simulation algorithm which proceeds processing each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.

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Mathematics Subject Classification: Primary: 65M06; Secondary: 90B20, 35L65, 34B45, 90B10.

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