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March  2006, 1(1): 57-84. doi: 10.3934/nhm.2006.1.57

Numerical approximations of a traffic flow model on networks

Gabriella Bretti 1, , Roberto Natalini 2, and  Benedetto Piccoli 3,

1. 

Department of Engineering of Information and Applied Mathematics, DIIMA, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy
2. 

Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico, 137, 00161, Roma, Italy
3. 

Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico 137, 00161 Roma

Received  September 2005 Revised  October 2005 Published  January 2006

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.
Keywords: finite difference schemes, boundary conditions., traffic flow, fluid-dynamic models, Scalar conservation laws.
Mathematics Subject Classification: Primary: 65M06; Secondary: 90B20, 35L65, 34B45, 90B1.
Citation: Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Numerical approximations of a traffic flow model on networks. Networks & Heterogeneous Media, 2006, 1 (1) : 57-84. doi: 10.3934/nhm.2006.1.57
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