A non-local pedestrian flow model accounting for anisotropic interactions and domain boundaries

Mathematical Biosciences and Engineering

卷:17

Raimund Bürger¹  Daniel Inzunza¹  Paola Goatin²  Luis Miguel Villada³ 

[1] 1. CI2MA and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile;

[2] 2. Inria Sophia Antipolis - Méditerranée, Université Côte d'Azur, Inria, CNRS, LJAD, 2004 route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex, France;

[3] 3. GIMNAP-Departamento de Matemáticas, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile and CI2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile;

关键词: non-local conservation laws;    macroscopic pedestrian flow models;    bounded domains;    anisotropic interactions;    high-resolution weno schemes;   

DOI  :  10.3934/mbe.2020314

来源: DOAJ

【 摘 要 】

This study revises the non-local macroscopic pedestrian flow model proposed in [R. M. Colombo, M. Garavello, and M. Lécureux-Mercier. A class of nonlocal models for pedestrian traffic. Math. Models Methods Appl. Sci., 22(4):1150023, 2012] to account for anisotropic interactions and the presence of walls or other obstacles in the walking domain. We prove the well-posedness of this extended model and we apply high-resolution numerical schemes to illustrate the model characteristics. In particular, numerical simulations highlight the role of different model parameters in the observed pattern formation.

【 授权许可】

Unknown