Traffic flow models with non-local flux and extensions to networks | Vidéo | Carmin.tv

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Traffic flow models with non-local flux and extensions to networks

By Simone Göttlich

Appears in collection : Foules : modèles et commande / Crowds: Models and Control

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.

Information about the video

Date of recording 06/06/2019
Date of publication 25/06/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19534703
Cite this video Göttlich, Simone (06/06/2019). Traffic flow models with non-local flux and extensions to networks. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19534703
URL https://dx.doi.org/10.24350/CIRM.V.19534703

Domain(s)

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

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/1927/Slides/Goettlich.pdf

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