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H 1 Darcy problem and crowd motion modeling

Auteurs : Maury, Bertrand (Auteur de la Conférence)
CIRM (Editeur )

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Darcy equations microscopic crowd motion models macroscopic crowd motion models Darcy problem and crowd motion modeling - numerical illustrations Questions

Résumé : We describe here formal analogies between the Darcy equations, that describe the flow of a viscous fluid in a porous medium, and some problems arising from the handing of congestion in crowd motion models.
At the microscopic level, individuals are identified to rigid discs, and the dual handling of the non overlapping constraint leads to discrete Darcy-like equations with a unilateral constraint that involves the velocities and interaction pressures, and that are set on the contact network. At the macroscopic level, a similar problem is obtained, that is set on the congested zone.
We emphasize the differences between the two settings: at the macroscopic level, a straight use of the maximum principle shows that congestion actually favors evacuation, which is in contradiction with experimental evidence. On the contrary, in the microscopic setting, the very particular structure of the discrete differential operators makes it possible to reproduce observed "Stop and Go waves", and the so called "Faster is Slower" effect.

Codes MSC :
34A60 - Differential inclusions [See also 49J21, 49K21]
34D20 - Stability of ODE
35R70 - PDE with multivalued right-hand sides
70E55 - Dynamics of multibody systems
35F31 - Initial-boundary value problems for nonlinear first-order equations
70E50 - Stability problems

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 11/08/15
    Date de captation : 03/08/15
    Collection : Research talks ; Partial Differential Equations ; Dynamical Systems and Ordinary Differential Equations ; Mathematical Physics
    Format : QuickTime (.mov) Durée : 01:07:45
    Domaine : Mathematical Physics ; Dynamical Systems & ODE ; PDE
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2015-08-03_Maury.mp4

Informations sur la rencontre

Nom de la rencontre : CEMRACS: Coupling multi-physics models involving fluids / CEMRACS : Couplage de modèles multi-physiques impliquant les fluides
Organisateurs de la rencontre : Frénod, Emmanuel ; Maitre, Emmanuel ; Rousseau, Antoine ; Salmon, Stéphanie ; Szopos, Marcela
Dates : 20/07/15 - 28/08/15
Année de la rencontre : 2015
URL Congrès : http://conferences.cirm-math.fr/1278.html

Citation Data

DOI : 10.24350/CIRM.V.18802703
Cite this video as: Maury, Bertrand (2015). Darcy problem and crowd motion modeling. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18802703
URI : http://dx.doi.org/10.24350/CIRM.V.18802703


  • Faure, S., & Maury, B. (2015). Crowd motion from the granular standpoint. Mathematical Models & Methods in Applied Sciences, 25(3), 463-493 - http://dx.doi.org/10.1142/S0218202515400035

  • Maury, B. (2014). Non smooth evolution models in crowd dynamics: mathematical and numerical issues. In A. Muntean, & F. Toschi (Eds.), Collective Dynamics from Bacteria to Crowds: An Excursion Through Modeling, Analysis and Simulation (pp. 47-73). Vienna: Springer.(CISM International Centre for Mechanical Sciences, 553) - http://dx.doi.org/10.1007/978-3-7091-1785-9_2

  • Maury, B., Roudneff-Chupin, A., Santambrogio, F., & Venel, J. (2011). Handling congestion in crowd motion modeling. Networks and Heterogeneous Media, 6(3), 485-519, electronic only - http://dx.doi.org/10.3934/nhm.2011.6.485

  • Maury, B., & Venel, J. (2011). A discrete contact model for crowd motion. ESAIM, Mathematical Modelling and Numerical Analysis, 45, (1), 145-168 - http://dx.doi.org/10.1051/m2an/2010035