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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.
Keywords : non-local scalar conservation laws; Godunov scheme
Codes MSC : Keywords : 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 arXiv category : Numerical Analysis ; Analysis of PDEs Domaine : Numerical Analysis & Scientific Computing ; PDE Format : MP4 (.mp4) - HD Durée : 00:43:59 Audience : Researchers Download : https://videos.cirm-math.fr/2019-06-06_Gottlich.mp4 
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Outreach
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 Congrès : 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 |
Voir aussi
- [Multi angle] Bottlenecks and rewards - adding fuel to the fire / Auteur de la Conférence Seyfried, Armin.
- [Multi angle] Equilibria and regularity in Mean Field Games with density penalization or constraints / Auteur de la Conférence Santambrogio, Filippo.
- [Multi angle] (In)efficiency in mean field games / Auteur de la Conférence Cardaliaguet, Pierre.
- [ Post-edited] Graphon mean field games and the GMFG equations / Auteur de la Conférence Caines, Peter E..
Bibliographie
- AGGARWAL, Aekta, COLOMBO, Rinaldo M., et GOATIN, Paola. Nonlocal systems of conservation laws in several space dimensions. SIAM Journal on Numerical Analysis, 2015, vol. 53, no 2, p. 963-983. - https://doi.org/10.1137/140975255
- 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
- COCLITE, Giuseppe Maria, GARAVELLO, Mauro, et PICCOLI, Benedetto. Traffic flow on a road network. SIAM journal on mathematical analysis, 2005, vol. 36, no 6, p. 1862-1886. - https://doi.org/10.1137/S0036141004402683
- 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
