Numerical approximations of a traffic flow model on networks
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Department of Engineering of Information and Applied Mathematics, DIIMA, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA)
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Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico, 137, 00161, Roma
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3.
Istituto per le Applicazioni del Calcolo "M. Picone", IAC-CNR, Viale del Policlinico 137, 00161 Roma
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Received:
01 September 2005
Revised:
01 October 2005
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Primary: 65M06; Secondary: 90B20, 35L65, 34B45, 90B10.
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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.
Citation: Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Numerical approximations of a traffic flow model on networks[J]. Networks and Heterogeneous Media, 2006, 1(1): 57-84. doi: 10.3934/nhm.2006.1.57
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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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