Kinetic BGK model for a crowd: Crowd characterized by a state of equilibrium

Abdelghani El Mousaoui; Pierre Argoul; Mohammed El Rhabi; Abdelilah Hakim

Applications of Mathematics (2021)

  • Volume: 66, Issue: 1, page 145-176
  • ISSN: 0862-7940

Abstract

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This article focuses on dynamic description of the collective pedestrian motion based on the kinetic model of Bhatnagar-Gross-Krook. The proposed mathematical model is based on a tendency of pedestrians to reach a state of equilibrium within a certain time of relaxation. An approximation of the Maxwellian function representing this equilibrium state is determined. A result of the existence and uniqueness of the discrete velocity model is demonstrated. Thus, the convergence of the solution to that of the continuous BGK equation is proven. Numerical simulations are presented to validate the proposed mathematical model.

How to cite

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El Mousaoui, Abdelghani, et al. "Kinetic BGK model for a crowd: Crowd characterized by a state of equilibrium." Applications of Mathematics 66.1 (2021): 145-176. <http://eudml.org/doc/297315>.

@article{ElMousaoui2021,
abstract = {This article focuses on dynamic description of the collective pedestrian motion based on the kinetic model of Bhatnagar-Gross-Krook. The proposed mathematical model is based on a tendency of pedestrians to reach a state of equilibrium within a certain time of relaxation. An approximation of the Maxwellian function representing this equilibrium state is determined. A result of the existence and uniqueness of the discrete velocity model is demonstrated. Thus, the convergence of the solution to that of the continuous BGK equation is proven. Numerical simulations are presented to validate the proposed mathematical model.},
author = {El Mousaoui, Abdelghani, Argoul, Pierre, El Rhabi, Mohammed, Hakim, Abdelilah},
journal = {Applications of Mathematics},
keywords = {discrete kinetic theory; crowd dynamics; BGK model; semi-Lagrangian schemes},
language = {eng},
number = {1},
pages = {145-176},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Kinetic BGK model for a crowd: Crowd characterized by a state of equilibrium},
url = {http://eudml.org/doc/297315},
volume = {66},
year = {2021},
}

TY - JOUR
AU - El Mousaoui, Abdelghani
AU - Argoul, Pierre
AU - El Rhabi, Mohammed
AU - Hakim, Abdelilah
TI - Kinetic BGK model for a crowd: Crowd characterized by a state of equilibrium
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 145
EP - 176
AB - This article focuses on dynamic description of the collective pedestrian motion based on the kinetic model of Bhatnagar-Gross-Krook. The proposed mathematical model is based on a tendency of pedestrians to reach a state of equilibrium within a certain time of relaxation. An approximation of the Maxwellian function representing this equilibrium state is determined. A result of the existence and uniqueness of the discrete velocity model is demonstrated. Thus, the convergence of the solution to that of the continuous BGK equation is proven. Numerical simulations are presented to validate the proposed mathematical model.
LA - eng
KW - discrete kinetic theory; crowd dynamics; BGK model; semi-Lagrangian schemes
UR - http://eudml.org/doc/297315
ER -

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