English
Traffic flow models with non-local flux and extensions to networks
Multi angle
Auteurs : Göttlich, Simone (Auteur de la conférence)
CIRM (Editeur )
35L65 - Conservation laws
65M12 - Stability and convergence of numerical methods (IVP of PDE)
90B20 - Traffic problems
Ressources complémentaires :
https://crowds2019.sciencesconf.org/data/pages/Crowds_book.pdf
https://www.cirm-math.fr/RepOrga/1927/Slides/Goettlich.pdf
CIRM (Editeur )
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Résumé :
We present a Godunov type numerical scheme for a class of scalar conservation laws with nonlocal flux arising for example in traffic flow modeling. The scheme delivers more accurate solutions than the widely used Lax-Friedrichs type scheme and also allows to show well-posedness of the model. In a second step, we consider the extension of the non-local traffic flow model to road networks by defining appropriate conditions at junctions. Based on the proposed numerical scheme we show some properties of the approximate solution and provide several numerical examples.
Mots-Clés : non-local scalar conservation laws; Godunov scheme
Codes MSC : Mots-Clés : non-local scalar conservation laws; Godunov scheme
35L65 - Conservation laws
65M12 - Stability and convergence of numerical methods (IVP of PDE)
90B20 - Traffic problems
Ressources complémentaires :
https://crowds2019.sciencesconf.org/data/pages/Crowds_book.pdf
https://www.cirm-math.fr/RepOrga/1927/Slides/Goettlich.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 25/06/2019 Date de Captation : 06/06/2019 Sous Collection : Research talks Catégorie arXiv : Numerical Analysis ; Analysis of PDEs Domaine(s) : Analyse Numérique & Calcul Formel ; EDP Format : MP4 (.mp4) - HD Durée : 00:43:59 Audience : Chercheurs Download : https://videos.cirm-math.fr/2019-06-06_Gottlich.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Foules : modèles et commande / Crowds: Models and ControlOrganisateurs de la Rencontre : Morancey, Morgan ; Piccoli, Benedetto ; Rossi, Francesco ; Wolfram, Marie-Thérèse Dates : 03/06/2019 - 07/06/2019 Année de la rencontre : 2019 URL de la Rencontre : https://conferences.cirm-math.fr/1927.html
Données de citation
DOI : 10.24350/CIRM.V.19534703Citer cette vidéo: Göttlich, Simone (2019). Traffic flow models with non-local flux and extensions to networks. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19534703 URI : http://dx.doi.org/10.24350/CIRM.V.19534703 |
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Bibliographie
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- COLOMBO, Maria, CRIPPA, Gianluca, et SPINOLO, Laura V. Blow-up of the total variation in the local limit of a nonlocal traffic model. arXiv preprint arXiv:1808.03529, 2018. - https://arxiv.org/abs/1808.03529#
- CHIARELLO, Felisia Angela, FRIEDRICH, J., GOATIN, Paola, et al. A non-local traffic flow model for 1-to-1 junctions. 2019. - https://hal.inria.fr/hal-02142345
- CHIARELLO, Felisia Angela et GOATIN, Paola. Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel. ESAIM: Mathematical Modelling and Numerical Analysis, 2018, vol. 52, no 1, p. 163-180. - https://doi.org/10.1051/m2an/2017066
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- FRIEDRICH, Jan, KOLB, Oliver, et GÖTTLICH, Simone. A Godunov type scheme for a class of LWR traffic flow models with non-local flux. arXiv preprint arXiv:1802.07484, 2018. - https://arxiv.org/abs/1802.07484
- KARLSEN, Kenneth Hvistendahl et TOWERS, John D. Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition. Journal of Hyperbolic Differential Equations, 2017, vol. 14, no 04, p. 671-701. - https://doi.org/10.1142/S0219891617500229
