American Institute of Mathematical Sciences

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May  2006, 6(3): 427-448. doi: 10.3934/dcdsb.2006.6.427

Fast algorithms for the approximation 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)
2. 

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

Istituto per le Applicazioni del Calcolo, Viale del Policlinico 137, 00161 Rome, Italy

Received  November 2005 Revised  January 2006 Published  February 2006

New computation algorithms for a fluid-dynamic mathematical model of flows on networks are proposed, described and tested. First we improve the classical Godunov scheme (G) for a special flux function, thus obtaining a more efficient method, the Fast Godunov scheme (FG) which reduces the number of evaluations for the numerical flux. Then a new method, namely the Fast Shock Fitting method (FSF), based on good theorical properties of the solution of the problem is introduced. Numerical results and efficiency tests are presented in order to show the behaviour of FSF in comparison with G, FG and a conservative scheme of second order.
Keywords: fluid-dynamic models, Scalar conservation laws, traffic flow, finite difference schemes..
Mathematics Subject Classification: 65M06; Secondary: 90B20, 35L65, 90B1.
Citation: Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Fast algorithms for the approximation of a traffic flow model on networks. Discrete & Continuous Dynamical Systems - B, 2006, 6 (3) : 427-448. doi: 10.3934/dcdsb.2006.6.427
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