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KINETIC BGK MODEL FOR A CROWD: CROWD CHARACTERIZED BY A STATE OF EQUILIBRIUM

Authors
  • El Mousaoui, Abdelghani
  • Argoul, Pierre
  • El Rhabi, Mohammed
  • Hakim, Abdelilah
Publication Date
Oct 21, 2020
Identifiers
DOI: 10.21136/AM.2020.0153-19
OAI: oai:HAL:hal-02985270v1
Source
HAL-INRIA
Keywords
Language
English
License
Unknown
External links

Abstract

In this paper we are interested in a dynamic description of the collective pedestrian motion based on the kinetic model of Bathnagar-Gross-Krook (BGK). In this model a pedestrians trend towards a state of equilibrium in a certain relaxation time is modeled. An approximation of the Maxwellian function that represents this equilibrium state is determined. A result of existence and uniqueness of the discrete velocity model is demonstrated. Thus the convergence of the solution to the solution of the continuous BGK equation is proven. Numerical tests are developed to validate the proposed mathematical model.

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