Citation

Bürger R, Goatin P, Inzunza D, Villada LM. Math. Biosci. Eng. 2020; 17(5): 5883-5906.

Copyright

(Copyright © 2020, American Institute of Mathematical Sciences)

DOI

10.3934/mbe.2020314

PMID

33120581

Abstract

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.

Language: en

Keywords

anisotropic interactions; bounded domains; high-resolution WENO schemes; macroscopic pedestrian flow models; non-local conservation laws