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

Raimund Bürger; Paola Goatin; Daniel Inzunza; Luis Miguel Villada; Raimund Bürger; Paola Goatin; Daniel Inzunza; Luis Miguel Villada

doi:10.3934/mbe.2020314

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5883-5906. doi: 10.3934/mbe.2020314

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

1.
CI2MA and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile
2.
Inria Sophia Antipolis - Méditerranée, Université Côte d'Azur, Inria, CNRS, LJAD, 2004 route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex, France
3.
GIMNAP-Departamento de Matemáticas, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile and CI2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Received: 31 May 2020 Accepted: 17 August 2020 Published: 03 September 2020

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.
- non-local conservation laws,
- macroscopic pedestrian flow models,
- bounded domains,
- anisotropic interactions,
- high-resolution WENO schemes
Citation: Raimund Bürger, Paola Goatin, Daniel Inzunza, Luis Miguel Villada. A non-local pedestrian flow model accounting for anisotropic interactions and domain boundaries[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5883-5906. doi: 10.3934/mbe.2020314

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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.

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