Applications of Mathematics, Vol. 66, No. 1, pp. 145-176, 2021
Kinetic BGK model for a crowd: Crowd characterized by a state of equilibrium
Abdelghani El Mousaoui, Pierre Argoul, Mohammed El Rhabi, Abdelilah Hakim
Received June 17, 2019. Published online October 21, 2020.
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.
Affiliations: Abdelghani El Mousaoui (corresponding author), School of Industrial Management, Mohammed VI Polytechnic University, Lot 660, Hay Moulay Rachid, 43150 Ben Guerir, Morocco, e-mail: firstname.lastname@example.org; Pierre Argoul, Laboratoire Ville Mobilité Transport, Université Gustave Eiffel, IFSTTAR, ENPC, F-77447 Marne-la-Vallée, France, e-mail: email@example.com; Mohammed El Rhabi, INTERACT Research Unit, Institut PolyTechnique UniLaSalle, 3 Rue du Tronquet, 76130 Mont-Saint-Aignan, France, e-mail: firstname.lastname@example.org; Abdelilah Hakim, Laboratory of Applied Mathematics and Computer Science, Faculty of Sciences and Technologies of Marrakech, Cadi Ayyad University, BP 549, Av. Abdelkrim El Khattabi, Guéliz, Marrakech, Morocco, e-mail: email@example.com