Kinetic BGK model for a crowd: Crowd characterized by a state of equilibrium - École des Ponts ParisTech Access content directly
Journal Articles Applications of Mathematics Year : 2021

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

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.
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Dates and versions

hal-02985270 , version 1 (02-11-2020)

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Abdelghani El Mousaoui, Pierre Argoul, Mohammed El Rhabi, Abdelilah Hakim. Kinetic BGK model for a crowd: Crowd characterized by a state of equilibrium. Applications of Mathematics, 2021, 66 (1), pp.145-176. ⟨10.21136/AM.2020.0153-19⟩. ⟨hal-02985270⟩
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