Français
Traffic flow models with non-local flux and extensions to networks
Multi angle
Authors : Göttlich, Simone (Author of the conference)
CIRM (Publisher )
35L65 - Conservation laws
65M12 - Stability and convergence of numerical methods (IVP of PDE)
90B20 - Traffic problems
Additional resources :
https://crowds2019.sciencesconf.org/data/pages/Crowds_book.pdf
https://www.cirm-math.fr/RepOrga/1927/Slides/Goettlich.pdf
CIRM (Publisher )
Loading the player...
|
Abstract :
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
MSC Codes : Keywords : non-local scalar conservation laws; Godunov scheme
35L65 - Conservation laws
65M12 - Stability and convergence of numerical methods (IVP of PDE)
90B20 - Traffic problems
Additional resources :
https://crowds2019.sciencesconf.org/data/pages/Crowds_book.pdf
https://www.cirm-math.fr/RepOrga/1927/Slides/Goettlich.pdf
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 25/06/2019 Conference Date : 06/06/2019 Subseries : Research talks arXiv category : Numerical Analysis ; Analysis of PDEs Mathematical Area(s) : Numerical Analysis & Scientific Computing ; PDE Format : MP4 (.mp4) - HD Video Time : 00:43:59 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-06-06_Gottlich.mp4 
|
Information on the Event
Event Title : Foules : modèles et commande / Crowds: Models and ControlEvent Organizers : Morancey, Morgan ; Piccoli, Benedetto ; Rossi, Francesco ; Wolfram, Marie-Thérèse Dates : 03/06/2019 - 07/06/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/1927.html
Citation Data
DOI : 10.24350/CIRM.V.19534703Cite this video as: 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 |
See Also
- [Multi angle] Bottlenecks and rewards - adding fuel to the fire / Author of the conference Seyfried, Armin.
- [Multi angle] Equilibria and regularity in Mean Field Games with density penalization or constraints / Author of the conference Santambrogio, Filippo.
- [Multi angle] (In)efficiency in mean field games / Author of the conference Cardaliaguet, Pierre.
- [Post-edited] Graphon mean field games and the GMFG equations / Author of the conference Caines, Peter E..
Bibliography
- 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
