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| HAL : hal-00537268, version 1 |
| Fiche détaillée |  Récupérer au format |
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| SIAM Journal on Applied Mathematics 71, 1 (2011) 107-127 |
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| A general phase transition model for vehicular traffic |
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| Sebastien Blandin 1Dan Work 1 |
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| (2011) |
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| An extension of the Colombo phase transition model is proposed. The congestion phase is described by a two-dimensional zone defined around an equilibrium flux known as the classical fundamental diagram. General criteria to build such a set-valued fundamental diagram are enumerated, and instantiated on several equilibrium fluxes with different concavity properties. The solution of the Riemann problem in the presence of phase transitions is obtained through the construction of a Riemann solver, which enables the definition of the solution of the Cauchy problem using wavefront tracking. The free-flow phase is described using a Newell-Daganzo fundamental diagram, which allows for a more tractable definition of phase transition compared to the original Colombo phase transition model. The accuracy of the numerical solution obtained by a modified Godunov scheme is assessed on benchmark scenarios for the different flux functions constructed. |
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| 1 : | Department of Civil and Environmental Engineering [University of California] (CEE) |
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University of California, Berkeley |
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| 2 : | Institut de Mathématiques de Toulon et du Var (IMATH) |
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Université Sud Toulon Var : EA2134 |
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| 3 : | OPALE (INRIA Sophia Antipolis / INRIA Grenoble Rhône-Alpes) |
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INRIA – CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS] |
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| 4 : | Istituto per le Applicazioni del Calcolo "Mauro Picone" (IAC) |
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Consiglio Nazionale delle Ricerche |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Partial differential equations – Hyperbolic systems of conservation laws – Macroscopic highway traffic flow model – Phase transition – Numerical scheme – Riemann solver |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00537268, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00537268 | |
| oai:hal.archives-ouvertes.fr:hal-00537268 | |
| Contributeur : Paola Goatin | |
| Soumis le : Jeudi 18 Novembre 2010, 09:09:01 | |
| Dernière modification le : Jeudi 3 Novembre 2011, 22:14:10 | |
