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H 1 Traffic flow models with non-local flux and extensions to networks

Auteurs : Göttlich, Simone (Auteur de la Conférence)
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 :
    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
      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 25/06/2019
      Date de captation : 06/06/2019
      Collection : Research talks
      Format : MP4
      Durée : 00:43:59
      Domaine : Numerical Analysis & Scientific Computing ; PDE
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-06-06_Gottlich.mp4
    Informations sur la rencontre

    Nom de la rencontre : Foules : modèles et commande / Crowds: Models and Control
    Organisateurs 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

    Citation Data

    DOI : 10.24350/CIRM.V.19534703
    Cite 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

    Voir aussi

    Bibliographie

    1. 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

    2. 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#

    3. 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

    4. 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

    5. 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

    6. 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

    7. 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

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